We demonstrate a grating coupler using an asymmetric nonlinear dual-core fiber with a pair of long-period gratings (LPGs). Simple formulas for the achievement of 100% coupling efficiency and small sidelobes are derived. The passband exhibits steep band transitions. By launching high-intensity optical pumps to alter the refractive indices of the fiber cores through cross-phase modulation, a wavelength tunable LPG dual-core coupler can be realized.