Based on sublayer division and backward recursion algorithm, the nonlinear reflection spectra at normal and oblique incidence for one-dimensional photonic crystal (1DPC) with one Kerr nonlinear defect are investigated. When incident intensity is higher than the incident intensity threshold, the defect mode appears inclined curved multiple-valued features at certain wavelengths. Compared with the circumstances of normal incidence, the full width at half maximum (FWHM) of the TE wave becomes smaller and that of the TM wave becomes greater. The change of FWHM also arouses the change of the incident intensity threshold. For the 1DPC with third-order nonlinear coefficient χ(3)>0, the defect mode position would be determined by the incident angle and incident intensity together and the minimal separation angle of TE wave and TM wave is decreased with increasing the incident intensity. While for the 1DPC with third-order nonlinear coefficient χ(3)<0, the defect mode moves towards shortwave direction when increasing incident intensity or incident angle. Besides, the minimal separation angle of TE wave and TM wave is increased with increasing the incident intensity. This research provides a valuable reference to the design and application of polarization filters, optical sensors, tunable filters and so on.