Photoionization cross sections for the 2s22p34So ground state of the nitrogen-like Cr17+ ion have been obtained using the R-matrix method. Calculations are carried out in the LS coupling scheme with two sets of target states. In the first, the six target states, 3Pe, 5So, 3Do, 3Po, 3So and 2p43Pe, are constructed by using 1s, 2s and 2p atomic orbitals. In the second set these are represented by the extensive configuration interaction using 3s, 3p and 3d correlation orbitals. The initial bound and the final continuum state wavefunctions are represented consistently in terms of the R-matrix basis functions. The partial and total cross sections are obtained. The cross sections are dominated by Rydberg series of resonances converging onto higher thresholds. Some of these resonances have been analysed and their positions and widths are listed.