This paper presents a position control strategy of the end-point based on the trajectory planning for a second-order nonholonomic planar three-link underactuated manipulator with a passive middle joint. Firstly, the dynamics model is built, and according to the geometry relationship, a differential evolution algorithm is used to calculate all link target angles corresponding to the target position. Then, according to the couple relationship between the active joint and passive joint, the time scaling method and bidirectional method are used to plan two trajectories of the two active links, respectively. And we connect the two trajectories to be a whole admissible trajectory based on the genetic algorithm by optimizing the suitable middle angle of the first link. Finally, we design a sliding mode variable structure controller to track the whole admissible trajectory, which can achieve the control objective of the system from an initial position to a target position. Numerical simulation results show the effectiveness of the proposed control strategy.