Soft robots with a well-balanced performance in terms of dexterity, accuracy, and payload have a great potential for application. Balancing safe human-robot interaction with operation performance enables the use of soft robot in biomedical fields, among others, such as surgery, rehabilitation and elder care. In this letter, we present a rod-driven soft robot (RDSR) where the flexible rods embedded in the silicone-based body provide a double push-pull actuation, to satisfy the needs of balanced performance. The RDSR can realize multi DOFs movement with elongation, contraction and bending. For trajectory tracking, Gaussian process model enables RDSR to achieve more accurate motion control with an RMSE within 2.8 mm compared to the constant curvature model with that within 10.8 mm. Comparative experiments demonstrate that the workspace, vertical and lateral stiffness of the RDSR are up to 5, 2.6 and 5.2 times that of an analogous tendon-driven soft robot (TDSR), respectively. Additionally, the RDSR possesses the ability, that the TDSR does not have, to actively apply pushing perpendicular to an inclined plane. Based on numerical Jacobian matrix, the maximum force along target direction is greater than 4 N for a 30$^\circ$ plane. Furthermore, pick-and-place tests validate that our soft robot, with large workspace, precise and steady motion, is capable of conducting object manipulation tasks.