At the moment there aren't that many racing games on linux, apart from grid autosport you can give dirt showdown a try although it's a tad over the top with trick races, gymkhana events and a little overenthusiastic announcer.
Two futuristic racers: Distance is an interesting title, still in the early access but already playable and looking very good.
Vector 36 - another early access title, looks promising.
And apparently Dirt Rally is coming to linux too - but it's not yet officially confirmed.

The Release Calendar indicates Project Cars for this month (best guess).

If you are not scared of Wine or PlayOnLinux - I highly recommend DIRT 3 Complete Edition. I've completed it without an issue in 49 hours :).

Quoting: AnxiousInfusionThe Release Calendar indicates Project Cars for this month (best guess).

I don't think that Project CARS will even be released for Linux at all, the developer went very silent in the status of the port. This leaves just F1 2015 and DiRT: Rally as upcoming racing games for Linux that aren't arcade.

there is also:

http://www.iracing.com

if you into simulators more.

Free games I have played a lot:
*SuperTuxKart
*Trigger Rally
*Tux Racer

Unfortunately there are not many racing games on Linux. (linux gaming as I said before is uneven with categories with plenty of excellent games and categories with too few games and racing games we have too few yet.

From non-free I have
*Race The Sun
This is actually good although not exactly what you are probably looking.

I do not have and is on early access but I've seen good opinions:
*Distance

Thanks for all your subjestions.

but what I looking for is something arcade-simulation (like grid autosport) or pure simulation, and full linux native, the most feasible option seems to be project cars, but apparently there's very few options to see it on linux

Quoting: AnxiousInfusionThe Release Calendar indicates Project Cars for this month (best guess).

I've removed that from the calendar, as I consider it completely MIA with it likely not coming.