An implicit finite difference time domain (FDTD) method is developed to analyze periodic structures at oblique incidence. The split-field technique is applied to the locally one-dimensional (LOD) FDTD method with the periodic boundary condition. In addition, the dispersion control parameters are introduced to reduce the numerical dispersion error. The effectiveness of the present method is investigated through the analysis of a photonic band gap structure. It is shown that the computational time is reduced to ≅16% of that of the explicit FDTD method with acceptable results being maintained. As an application, a broadband mirror consisting of a subwavelength grating is analyzed and discussed.