The scattering of electromagnetic waves by a dielectric grating with planar slanted-fringe is analyzed using the improved Fourier series expansion method. In the analysis, the slanted grating region is divided into layers to make an assembly of stratified thin modulated index layers. This method can be applied to a wide range of periodic structures and is especially effective in the case of planar slanted grating, because the electromagnetic fields in the each layer can easily be obtained by shifting the solution in the first layer. In this paper, the numerical results are given for grating with rectangular and sinusoidal dielectric profiles, and for TM and TE cases of arbitrary incident angle. The diffraction efficiencies obtained by the presented method are compared with the results by the coupled-wave approach; the influences of the slant angle on the diffraction efficiencies at the Wood's anomaly and at the coupling resonance frequency are also discussed.