This article presents an analytical solution of the effective index of the fundamental waveguide mode of one- dimensional (1D) metallodielectric grating for TM polarization. In contrast to the existing numerical solution involving a transcendental equation, it is shown that the square of the effective index ( $n_{\text{Eff}}$ ) of the fundamental waveguide mode of 1D grating is inversely proportional to the slit width (w) and the refractive index ( $n_m$ ) of the ridge material and varies linearly with the incident wavelength (λ). Further, it has also been demonstrated that the dependence of $n_{\text{Eff}}$ on the grating period (P) and the incidence angle (θ) is minimal. Agreement between the results obtained using the solution presented in this article and published data is excellent.