I have a site www.mysite.com and it has a subdomain secure.mysite.com. Now I want to order a SSL cert for this subdomain but I found that there is no place in Plesk to generate/install cert for subdomain. Should I just use the Certificate page of the main domain and specify secure.mysite.com as the cert domain name, or I have to create a new site with secure.mysite.com domain name?

No. Delete the submain and create it as a normal site. ie secure.domain.com as a normal site. Then you will see the ssl options. As a side note you need to make sure you have a static IP for that domain to use the with a ssl cert.

Are you sure for this? One of my server uses Godaddy cert and Cpanel. The secure site is shared IP site. Must I have a IP address for secure site under Plesk?

fairly sure. Last time I check SSL required a static IP. Although it may be possible. But I do know you must create the domain as a versus a subdomain.

Which version of Plesk are you talking about? I see subdmain SSL option in Plesk 8.0 panel. There is no such option in Plesk 7.

I have got plesk 8. I saw this option as well although I did not manage to find away to use it and insert the cert. Their maybe I did not take the time to read the manual on it. I do however know the method I stated works in plesk 7 and plesk 8.

There is generate cert option in the main domain page. Maybe I can just put the subdomain name into the domain box to generate cert for subdomain?

Yes there will be a section to generate CSR and all the needed data.i believe there is a how to on the ev1 site under SSL's or even on the godaddy site on how to request and setup SSL.