The R-matrix method has been applied to calculate photoionization cross sections for the 2s22p34S0 ground state of the N-like Al6+ ion. To test the accuracy of results, calculations are carried out in the LS coupling scheme with two sets of target states and results were obtained in both the length and velocity formulations. In the first, the six target states, 3Pe, 5S0, 3D0, 3P0, 3S0 and 2p43Pe, are constructed by using 1s, 2s and 2p atomic orbitals. In the second set these states are represented by extensive configuration interaction using 3s, 3p and 3d correlation orbitals in addition to the spectroscopic ones. The partial and total cross sections are obtained. The cross sections are dominated by Rydberg series of resonances converging onto higher thresholds of Al7+. Some prominent resonances have been analysed and their positions and widths are listed.