2-dimensional scattering problem of electromagnetic waves by a periodic strip grating on a grounded dielectric slab in case of oblique incidence and arbitrary polarization is analyed by the vector Floquet modal expansion method. Solution convergence versus number of Chebyshev polynomial terms representing the unknown strip current density and number of space harmonics is examined, and some numerical results such as variation of power of significant space harmonics(scattered mode) are compared with those obtained by previous method. In particaluar, the relationship between Bragg blazing phonmena and characteristics mode(current) on the srip is discussed in detail.