I translate the categories to another language, but in the main page, the two language categories are all displayed. How can I filter another language? My WPML version is 2.4.1. I found all the categories are displayed on my theme, is there any way I can get the correspondence between the different language categories, so I can filter it.
First you should upgrade WPML to the latest version, which is 2.4.3 at time of writing.
To properly translate categories you should start by editing the category of the default language. Once you are in that screen (
Have you created categories for both languages ? eg. if you have blog category in english then you have to create same as for other language. same for posts.
If yes, then please check if language code filters is applied to archive page or not. if not then you have to make filter for language code.