This paper focuses on the model reference state unilateral tracking control problem of positive switched systems. The state unilateral tracking means that the state always keeps in the same direction of the reference objective, either above or below. This feature makes unilateral tracking play a role of avoiding the overshoot. Via the dual design of both the controller and the switching signal, the state unilateral tracking control problem with L-1-gain performance for positive switched systems is solved through adopting multiple linear co-positive Lyapunov functions technique. The design method is applicable to the case that the unilateral tracking control problem is unsolvable for any subsystem of a positive switched system. Moreover, two techniques are presented in order to deal with the state unilateral tracking problem. Finally, a practical example demonstrates the validity of the presented result.