In this paper we propose a Galerkin's method for the hydroelastic problem of a rectangular plate on shallow water in waves. The bi-directional complex Fourier series are adopted as a displacement function of the rectangular plate, which complex conjugates are adopted as weighting functions. The weighted residual method leads to the weak form to be solved. On the plate boundary, the weak form should be combined with Boundary Element Method. A boundary element, in which two nodes are arranged at two Gauss-Legendre integral points, is proposed to obtain the same results as 3rd order polynomial interpolation. Present Galerkin's method can calculate large ratio of plate length and incident wavelength quickly.