Solving coupling-wave differential equations with boundary-value conditions is a basic method for investigating waveguide mode converters with varying radius or bent axis. A matrix method according to microwave net theory is presented to make the solution simple and explicit with clearer physical meanings. For a group of coupling-wave differential equations in which N coupling waveguide modes are considered, the transmitting matrix and scattering matrix of the converter described by the equations can be obtained by solving the differential equations 2N times with different initial value conditions, respectively. Then with use of the scattering matrix, the solution of the coupling-wave differential equations with boundary-value conditions can be educed.