We study the mass spectra of hidden-charm pentaquarks having spin J = We systematically construct all the relevant local hiddencharm pentaquark currents, and we select some of them to perform QCD sum rule analyses. We find that the P c (4380) and P c (4450) can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find (a) the lowest-lying hidden-charm pentaquark state of J P = 1/2 − has the mass 4.33 +0.17 −0.13 GeV, while the one of J P = 1/2 + is significantly higher, that is, around 4.7-4.9 GeV; (b) the lowest-lying hidden-charm pentaquark state of J P = 3/2 − has the mass 4.37 +0.18 −0.13 GeV, consistent with the P c (4380) of J P = 3/2 − , while the one of J P = 3/2 + is also significantly higher, that is, above 4.6 GeV; (c) the hidden-charm pentaquark state of J P = 5/2 − has a mass around 4.5-4.6 GeV, slightly larger than the P c (4450) of J P = 5/2 + .