As you have now mentionned that your computer can actually keep up (at 150 fps no less), I suspect you have a case of temporal aliasing.
The problem is that 150 is not a multiple of 60. Let's say we look at one tenth of a second. That's 15 frames generated by your computer but only 6 can be shown on your screen. The frames you will see will probably be something like:
#1 - #3 - #6 - #8 - #11 - #13
Notice how the increment is +2, +3, +2, +3. This will cause animation to not look smooth. There is no steady increment which will let you display 60 frames out of 150.
As I wrote in the comments below, forcing the game to run at "only" 120Hz should help as the screen should show every other frame.
Enabling vsync is even more reliable but it seems your game does not deal well with latency then.
By the way, that's why serious gaming monitors now have adaptive refresh rates. They just show the frames when they're ready and have none of the above issues.