It's hard to tell from the little information in your post, but most tiny babies sleep soundly for maybe 2-3 hours at the longest before they need to eat again. And most babies sleep much better when in contact with mommy.
There's also a common startle reflex during sleep: their arms jerk as if they think they're falling, or they hit themselves in the face and wake up. Swaddling helps with this.
If your baby is squirming around as if uncomfortable, he probably is. He could be too hot or cold, or have unburped air in his tummy, or have a very sensitive digestive system and be feeling gas or food moving through. Maybe something is poking or pinching his skin. Check to see that he doesn't have a hair wound around a finger or toe.
Reflux is a common problem, too, and propping him up a bit during sleep, and feeding him with his head held higher, may be helpful.
Good luck. Some babies just don't sleep well, for up to their first two years. Everytime the tired parents think they've worked it out, things change and a new pattern sets in. It's just one of the toughest things about parenting.