Hi, is there anyway I can implement gallery category ?

I need a site with this structure:
Category 1
-> Gallery 1
--> Photo 1
--> Photo 2
-> Gallery 2
--> Photo 3
--> Photo 4
Category 2
-> Gallery 3
--> Photo 5
--> Photo 6
-> Gallery 4
--> Photo 7
--> Photo 8

Is that possible?

Did you even take a look at Zenphoto before asking??? Of course. That is called "album" on Zenphoto. Please see the glossary for the right terms to avoid confusion.

I mean like this:

Category 1
-> Album 1
--> Photo 1
--> Photo 2
-> Album 2
--> Photo 3
--> Photo 4
Category 2
-> Album 3
--> Photo 5
--> Photo 6
-> Album 4
--> Photo 7
--> Photo 8

In admin, I can't find gallery tab/menu.

ok, gallery is: The whole zenphoto installation including all albums.

And can I categorized my albums?

An album IS the category...you can have as much subalbums as your server has space.

I understand the problem, because the same is for me.
I make photographs, animations, and photo animations also.
I would like to have a gallery page with categories like: Photography and Animation. I would like my photo works to show up in Photography, the animation works in Animation, and photo animations in BOTH categories. Like categories for news.

There is only one parent of each album in Zenphoto now.

Albums are NOT like news categories. You need to understand that Zenphoto's albums are file system based, so they are static. So an image can be only in one album at the time.
If you wish an entry of album1 to appear in album2 you need to copy it. Thus you have two images of the same name in different albums.

The only other way is to use the dynamic album feature which is basically a saved search query. See the tutorial on our site.

I understand it. ;-) There are only static albums.
I WISH to use album categories.
Workaround for me: I use Zenphoto as a personal portfolio page. My almbums will not change. I only upload when a work is complete. So I do not publish albums, just news in news categories, and I put the thumnails into the news page.

No you didn't exactly. You can sort of achieve what you want by using dynamic albums. They are a bit different from "real" albums by definition though. Please take the time to read:
http://www.zenphoto.org/news/how-to-use-the-dynamic-albums-feature

I have the same problem. I need to categorize my pictures and albums such as wedding or nature photos so that user can select a category and see only albums that contain pictures of that category.
dynamic albums is not helping because i have to either use a naming convention to categorize my pictures this way or tag all the images which rises another problem; tags are shared between news, pages, albums and images.

ynamic albums is not helping because i have to either use a naming convention to categorize my pictures this way or tag all the images which rises another problem; tags are shared between news, pages, albums and images.

I don't understand. A dynamic album will never contain news and pages. It also will only contain albums if they match the search (in this case the same tags). Also you can disable album resutls for the search on the options while creating a dynamic album.

So either you create "normal" static albums which can be nested in endless levels since Zenphoto is filesystem based or you use dynamic albums which also can or not contain albums.

You can, of course, program your site to give your users specific search requests. These can even be dynamically assembled from whatever selection criteria you wish.

You simply create a post request for the search criteria that have been selected.