In what countries it is legal to host torrent traacker? I mean without future issues with laws like illegal movie, software downloading.
Hosting a torrent tracker should be legal anyplace; it's just software and has valid, legal, use cases. The problem is what files are being posted. The tracker software itself isn't any more illegal than the ftp client you could also use to transfer illegal software, etc. (As with all legal questions, if you really have concerns, you should probably talk to an actual lawyer or at least track down the relevant legal documents.) TorrentFreak follows BitTorrent-related news specifically and might be a good starting resource for you to get a feel for what the legal climate is like at the moment.
Your web host might notice that you're running tracker software and have some questions about that, but again if you're not supporting the distribution of illegal content, you should probably be okay overall as long as your hosting setup can support the application running. I'd imagine there are some hosts who might not want to run the risk at all and just ban such applications, but that's something that would have to be checked on a case by case basis. Refer to your terms of service or ask support.
If I were you I would consider Ukraine. IIRC for some time back then (in 90-s) they had a very liberal laws considering copyright but things could have changed. They, probably, do not have any laws (at least I could not find it) about "assisting in making copyright content available" activity which is usually incriminated to the torrent trackers.
I'd also checked other ex-USSR countries, again via google and google translate. Also, I'd visited some local sites and just asked people (google translate is your friend!). Belarus would be second on my list with Kazakhstan third.
Disclaimer. I'm against violation of the laws, but I do not agree with @Su and his mentioned here "illegal torrents". Those torrents may be illegal in some jurisdictions and not the others which is exactly the point OP was asking. He is the one who does not want to break the law!
You could just as well have asked: In what countries are videotapes legal? It is not the torrent tracker that is illegal or legal, that much I think is clear already.
So your question should rather be: In what countries do I run the least risk of getting caught for running a torrent tracker that might have content that can be reported or is illegal in most countries?
The countries are: France, Netherlands, Russia, Ukraine and USA. Yes USA. Other countries may or may not work fine, I am simply telling you what countries are widely used as of now by the larger and most popular trackers.
It all comes down to what torrents are uploaded on the tracker and the way you react as web site owner if you get a report that you have 'illegal content' on your server, and most important of all, the policies of the specific data center you use. Usually you can simply remove the reported torrent in question. They can not close your web site because you run a torrent tracker as that is not illegal, but they can close it because you have repeatedly ignored the complaints and have not removed content that was for example copyrighted.