I changed mgstr text of msgid "gallery" and made a customized zenphoto.mo using Poedit.
I put it into \zp-core\locale\ja_JP then refreshed web page.
However it dose not reflect my change on Index page.
Is my change process correct ?
What should I do?

Sorry, I forgot my purpose.
I want to change the text of h2 tag "Gallery" of index page.

If you use Poedit it will generate a .mo. and a .po file. The .mo file is used for the actual translation so you need to replace both existing ones.

I want to change the text of h2 tag "Gallery" of index page.

Well, what theme? Not all third party themes support gettext translation and not all strings are gettexted anyway. "Gallery" may also often the standard site title if you didn't name it otherwise.

EDIT: My colleague just reminded me: In PHP 7+ there seems to be an issue with refreshing changes in these file. This is as far as we know a PHP core / server side problem we cannot do anything about so far.

Apparently there's a bug in the Apaches' mod_perl module which causes translations not to work. You can try to disable the mod_perl module.
See: https://www.claudiokuenzler.com/blog/1023/php-gettext-translations-not-working-apache-mod_php-cli-works
This bug also affects our own current local MAMP environment.

Thanks a lot, Unfortunately my server service provider doesn't offer change of Apache definition. I did necessary changes of zenphotp.mo and re-installed. I am a little bit sad!!

We are too. This appears to be a rather new issue. Sadly there is nothing that can be done about this.