Either you're using paper that's too thick or you're using paper that your printer's rollers can't grip onto. (That's a problem that's previously been reported here with HP printers).
Are you using HP's own paper? If not, give it a go. I use HP Everyday Photo Paper because it's the best quality I've found (without paying for the real top-of-the range 'professional stuff) and I've not even got an HP printer! It's £13.99 for 100 (200gsm, glossy) sheets in Sainsbury's but you can get it cheaper elsewhere if you shop around.