The coupling equation set, which describes coupling characteristics of a multi-waveguides directional coupler, is transformed into a tridiagonal linear equation set by Laplace transform. And then general solution of this equation group is obtained by use of the chase method. Furthermore, given incidence condition, solution of the coupling equation group can be obtained exactly by inversion of the Laplace transform. Coupling characteristics of a five-waveguides directional coupler are studied in this method under two conditions of that light beam incidence upon one waveguide and five waveguides. And then analytic expressions of solution of the coupling equation group are obtained and variation curves of optical power in each waveguide are given. This method, which can be used to solve coupled-mode equations set of a multi-waveguides directional coupler with both any quantity of waveguides and any incidence condition, is significant for structure design of a multi-waveguides directional coupler.