This work investigates a fully-developed laminar flow of a complex channel with a period of 2d. Because of the character of symmetry, the study will focus on an L-shaped region. The governing equations are the Poisson equations. The analysis is solved by an eigenfunction expansion and the point-match method. The local velocity, the maximum velocity, the average velocity and the f. Re of the channel are discussed in the present paper. Furthermore, the results of present research are compared and discussed with the relevant references and it shows that the results will be helpful toward the proposals in the channel flow systems of recent patents.