I would use 500-piece dinosaur jigsaw puzzle.

Student or Learner
1. I bought a 500 pieces puzzle of dinosaurs for him.
2. I bought a 500 - piece puzzle of dinosaurs for him.
Are the above sentences correct grammatically?
Is there any other suggestion, please?
Thanks.
I would use 500-piece dinosaur jigsaw puzzle.
It would be most natural to say I bought him a 500-piece dinosaur puzzle. Note that there are no spaces around the hyphen.
I am not a teacher.
I'd include the word "jigsaw" as Tdol did (if that's what the OP was referring to). A "500-piece dinosaur puzzle" could be a different kind of puzzle with 500 pieces.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
I don't think "jigsaw" is necessary here.
In American English, at least, the term "puzzle", in the context of having a set number of pieces, is assumed to be a jigsaw puzzle by default, unless it's further modified (e.g. "500-piece 3D puzzle").
Other puzzles are modified: "50 x 50 crossword puzzle", "chess puzzle", "word puzzle", "math puzzle", "picture puzzle", etc.
NOT A TEACHER. Translator and editor, and I hold a TESOL certificate. Native speaker of American English (West Coast)
We do often say jigsaw puzzle in BrE- it may be another of those little differences.