Optical couplers which are composed of three channel waveguides arranged two-dimensionally are investigated numerically. The mode-matching method that matches the boundary conditions in the sense of least squares is applied to this problem, using the hybrid-modal representation. The precise numerical results of the dispersion relations and field distributions are presented for the lowest three modes near the cutoff. The arrangement of three waveguides can be optimized so as to satisfy the condition for maximum power-transfer efficiency.