Problem of Tstringlist.indexof ....too slow

Why don't you simply use TSTringList.Duplicates :=  dupIgnore;

procedure TForm1.Button1Click(Sender: TObject);
var
  List : TStringList;
  i  : integer;
begin
  List := TStringList.Create;
  List.Duplicates := dupIgnore;
  List.Sorted := true;
  List.LoadFromFile('FileName'); //or just add NUM1 as text
   
  for i := 0 to List.Count - 1 do
  begin
    //DO whatever you want
  end;

  List.Free;
end;

@Ferruccio68, dupIgnore does nothing if the stringlist is not sorted. And if I understand correctly, this list cannot be sorted.

@hongkeng_woon, why did you ever decide to use a stringlist for storing numbers in the first place? It would be a lot easier if you would store them in a dynamic array of integers in the first place. Or a TList if using dynamic arrays is too complex for you. If you use numbers only, store them as numbers! Then the comparisons will be a lot faster too.
At http://www.workshop-alex.org/Sources/untDuplicateCheck.pas you will find an interesting unit called untDuplicateCheck, written by me. Basically, it provides a mechanism to check for duplicates, and it does this quite fast. Use something like:

var
  DuplicateChecker: IDuplicateChecker;
  I: Integer;
begin
  DuplicateChecker:= NewDuplicateChecker; // Parameters are all optional.
  for i:=0 to num1.count - 1 do begin
    if AddAndCheck(num1.strings[i]) then num2.add(num1.strings[i]);
  end;
  DuplicateChecker:= nil;
end;

Above code will probably perform "slightly" faster... ;-)

One minor warning, though... Speed comes at a price. My method will eat a lot of memory. It takes 10 megabytes of memory when active. But the memory will be freed again once you're done and assigned nil to the duplicate checker. It's the price you have to pay for a very neat speed increase...

if AddAndCheck(num1.strings[i]) then num2.add(num1.strings[i]);

Should be:

if DuplicateChecker.AddAndCheck(num1.strings[i]) then num2.add(num1.strings[i]);

Silly me... :-)

--> @Ferruccio68, dupIgnore does nothing if the stringlist is not sorted. And if I understand correctly, this list cannot be sorted.
Gosh,i've totally misreaded the question! :((

Well, just a test....
Using Pos instead of indexof seems to be more fast.
This is quite fast using listboxes, so i guess that using STringLIsts missing the drawing should be more fast again

procedure TForm1.Button1Click(Sender: TObject);
var
i,y: Integer;
begin
for i := 1 to 3 do
   for y := 1 to 10000 do
     if y mod 2 = 0 then
      Listbox1.Items.Add(inttostr(y))
     else
      Listbox1.Items.Insert(Y-1,inttostr(y))
end;

procedure TForm1.Button2Click(Sender: TObject);
var
i: Integer;
s: STring;
begin
for i := 0 to Listbox1.Items.Count-1 do
begin
  If pos(Listbox1.Items[i],s) = 0 then
   s := s+Listbox1.Items[i]+',';
 end;
 ListBox2.Items.CommaText := s;
end;

My solution avoids IndexOf completely.  SortCompare1 alphabetizes the list, and SortCompare2 restores the original sequence.  The original sequence is temporarily stuffed into the Objects property of the list, so this is only appropriate when you're not already using the Objects property.

You can remove the reference to   SL.CommaText; in my solution, it was only put in temporarily for debugging as the linker removed the method and I wanted to watch the sequence in the debugger.  I just forgot to remove it.

You can also remove the Assert.  Sorry about that.

suggest you change string to int as string compare is veryvery slow
the code is like below
I want to check the time it run but it runs so quick(not more than 1second) so I did not check the time

procedure TForm1.Button1Click(Sender: TObject);
var
  i,j:integer;
  s:string;
  dt:TDateTime;
  sl:TStrings;
  na:array[0..10000] of integer;
  found:boolean;
  tempi:integer;
begin
  s:='';
  s:=IntToStr(random(10000));
  for i := 2 to 10000 do
  begin
    s:=s+','+IntToStr(random(10000));
  end;
  dt:=Now;
  sl:=TStringList.Create;
  sl.QuoteChar:=',';
  sl.DelimitedText:=s;
  for i:=0 to sl.Count-1 do
  begin
    na[i]:=StrToInt(sl[i]);
  end;
  s:=IntToStr(na[0]);
  for i:=1 to sl.Count-1 do
  begin
    found:=false;
    for j:=i+1 to sl.Count-1 do
    begin
      if(na[j]=na[i])then
      begin
        found:=true;
        break;
      end;
    end;
      if not found then
      begin
        s:=s+','+IntToStr(na[i]);
      end;
  end;
AppliCation.MessageBox(PChar(s),'');
end;