By simultaneously taking field localization and slow light effects into account, in this paper we make use of a field averaging method to calculate the effective nonlinear refractive index coefficient (n2) of Kerr photonic crystals (PhCs) in the first band. Although the nonlinear PhC is beyond the traditional long-wavelength limit, interestingly, the theoretically calculated effective n2 agrees well with one numerically measured via the self-phase-modulation induced spectral broadening. Moreover, due to the cooperative influence of field localization and slow light effects, the effective n2 of the PhC decreases slowly at first and then goes up quickly with increasing frequency. This kind of dispersive nonlinearity is purely induced by the periodic nanostructures because the optical parameters of both components of the PhC we took are frequency-independent. Our results may pave the way for enhancing or limiting nonlinear effects and provide a method for producing the dispersive nonlinearity.