Abstract: Due to the inefficiency of traditional root-finding method and its dependence on initial value, in this paper, a multimodal expansion method is proposed to solve the problems of eigenvalues and eigenfunctions in the homogeneous ocean waveguide. The sine function is chosen as the orthogonal basis function of the sound pressure in the depth direction. The eigenvalues can be obtained by decomposing the matrix of the expansion coefficients together with the eigenfunctions rather than finding root in transcendental equation. Numerical validation of this method is carried out in the single-layer isovelocity waveguide, the waveguide with sound velocity profile and the double-layered waveguide and proves that this algorithm is reasonable and feasible.