The scattering of electromagnetic waves from a periodic dielectric interface is studied for a general angle of incidence. It is called conical diffraction in grating theory for the general case where the incident wave vector is not perpendicular to the ruling direction of the gratings. We adopt the electric and magnetic field components along the row direction as the two unknown scalar functions and reduce the vector nature of the problem to solving simple matrix equations to obtain the scattered fields. The extended boundary condition method is applied with the Fourier series expansion for the surface fields. For the special case of incidence angle perpendicular to the row direction, the results are reduced to those developed before. Numerical results are obtained to show that energy conservation and reciprocity are obeyed for scattering by sinusoidal surfaces for the general case. This serves to check the consistency of the formalism.