Dynamic control of soft robotic manipulators is an open problem yet to be well explored and analyzed. Most of the current applications of soft robotic manipulators utilize static or quasi-dynamic controllers based on kinematic models or linearity in the joint space. However, such approaches are not truly exploiting the rich dynamics of a soft-bodied system. In this paper, we present a model-based policy learning algorithm for closed-loop predictive control of a soft robotic manipulator. The forward dynamic model is represented using a recurrent neural network. The closed-loop policy is derived using trajectory optimization and supervised learning. The approach is verified first on a simulated piecewise constant strain model of a cable driven under-actuated soft manipulator. Furthermore, we experimentally demonstrate on a soft pneumatically actuated manipulator how closed-loop control policies can be derived that can accommodate variable frequency control and unmodeled external loads.