Try exiting the game, even exit and restart Steam maybe... right-click either or single/multiplayer in Steam and go to 'Properties' > 'Local Files' tab > 'Verify Integrity of Game Cache'... it should verify all files and update what you don't have... other than that you'll have to contact Steam support and verify your purchase confirmation, etc. with them if that doesn't work to relieve the problem...
Thanks to help
I contact Steam about that
Thank you for contacting Steam Support.
Please make sure that both Modern Warfare 3 Singleplayer and Multiplayer are installed. You should launch both components at least once.
If the issue still exists, browse to your Call of Duty: Modern Warfare 3 installation folder (Usually C:\Program files\Steam\Steamapps\common\call of duty modern warfare 3\) and delete the Zone folder.
Next, verify the GCF for this game as outlined here:
Title: Verifying Game Cache Files (GCF)
Note: Files may fail to verify. This is normal and can be ignored.
Exit Steam entirely, Reboot your computer, then test the issue.
If you are still having issues accessing the new DLC please do the following:
Navigate to your Steam directory (C:\Program Files\Steam\) and delete the AppCache folder.
Restart Steam and launch Call of Duty: Modern Warfare 3.
If you have any further questions, please let us know - we will be happy to assist you.