A plane coupler has been developed for a two-dimensional (2D) wireless power transmission. This coupler can construct a continuous wireless power transmission system for mobile devices due to its small, light characteristics. This coupler has two elements connected with a 2D waveguide sheet, and coupling capacitances between the elements and the sheet decrease the coupler size by reducing their resonance frequencies. A propagation loss of -10.0dB is obtained using the small 0.025-λ² coupler. Continuous operation of the mobile device is demonstrated by applying wireless power transmission to the 2D waveguide sheet with the small plane coupler.