How to solve the issue between ASDM and SSL connection with one JAVA in ASA?

remember to import the Cisco certificate, see further steps in link

When using some versions of Java, such as Version 7 update 51, the ASDM Launcher requires a trusted certificate. An easy approach to fulfill the certificate requirements is to generate a self-signed identity certificate and to configure the ASA to use it when establishing an SSL connection. After you generate the identity certificate and configure the ASA, you need to register it with the Java Control Panel on your computer.

For the ASA 5506-X, 5508-X, or 5516-X with an ASA FirePOWER module, you can use ASDM for module management. In this case, you must create two identity certificates: one for the ASA and one for the module.

http://www.cisco.com/c/en/us/td/docs/security/asdm/identity-cert/cert-install.html
More on the workarounds in ADSM 7.1(x) release notes - http://www.cisco.com/c/en/us/td/docs/security/asdm/7_1/release/notes/rn71.html#wp516584

also as same machine may be used to manage multiple ASA and the browser cache itself may trigger the issue, so In Java Control Panel's General tab sheet, there is the Temporary Internet Files. Typically removing all temp files will result in better functionality.

After downgrading to java6 and did some config based on what you said, ASDM begin to work. the client already is installed there. So just clicked it. It can work now. Thank you!