I am doing a thieve guild quest where I need to deliver Moon Sugar. The journal indicates his location nearby Markath, so I travel to Markath.

Then I checked again, he is now nearby Solitude, therefore I travel to Solitude.

And when I checked again, he is nearby Whiterun!

This is so irritating!!! If he is not too far away from me at the beginning, I will sprint to look for him. Now it is like endless loop.

Anyone know the pattern of his route so I can catch him?

I think he stays in that small camp by markarth overnight. That's how I caught him.

I take it you are fast traveling? chances are if you just straight bolt for him you will geto to him before he moves on as traveling normally is "quicker" because your not effected by the game time ( it seems it take 16hrs to travel from whiterun to riften when using fast travel)

or you can just fast travel somewhere infront of him and wait till he comes instead of chasing him