This paper presents a control strategy for the position and posture control of a planar four-link underactuated manipulator with a passive second link based on a back-propagation neural network (BPNN) model. First, using the differential evolution (DE) optimization algorithm, the target angles of all links are calculated. The third and fourth links are then controlled from their initial angles to zero. Next, the control process is divided into the following two steps: the control objective of the passive link is implemented in the first step, and the control objectives of the active links are implemented in the second step. In the first step, the system is reduced to a planar virtual Pendubot, a BPNN model based on the DE algorithm is trained to obtain the coupling relationship between the links of this Pendubot. This model gives the speed of the first link to move the passive link to approach the target angle. Then, a fuzzy controller is designed to indirectly control the passive link to its target angle. In the second step, the position mode of the servo controller is adopted to control all active links to their target angles. Experimental results verified the effectiveness of the proposed control strategy.