An improved three-dimensional (3-D) locally one-dimensional finite-difference time-domain (LOD-FDTD) method is developed and applied to the wideband analysis of waveguide gratings. First, the formulation is presented, in which dispersion control parameters are introduced to reduce the numerical dispersion error and perfectly matched layers are simply implemented without the field components being split. Next, as a preliminary calculation, the wavelength response of the waveguide grating is analyzed in a two-dimensional problem. The dispersion control contributes to the accuracy improvement even with a large time step beyond the Courant-Friedrich-Levy limit. Finally, a 3-D waveguide grating is analyzed. The use of the dispersion control parameters only in the propagation direction enables us to employ a large time step for efficient calculations, i.e., the computation time can be reduced to about half that of the explicit counterpart. In the Appendix, maximum time step for providing a highly accurate result is also predicted using the numerical dispersion analysis.