A high-resolution demultiplexing method is proposed for the separation of coaxial multiple orbital angular momentum (OAM) beams which are created by a self-designed computer-generated hologram (CGH) encoded with logarithmic spiral phases. The logarithmic spiral phase, consisting of both azimuthal and radial phase, enables the two-dimensional demultiplexing of the OAM beams. The simulation and experiment results show that, with our method, the coaxial multiple OAM beams can be effectively separated in the specified plane. The overlap between the adjacent channel is greatly reduced by the high-resolution demultiplexing method, which is based on an optical geometrical transform and a coherent copy technique. The proposed method has great potential in increasing the number of spatial channels available for OAM multiplexing transmission system.