The musculoskeletal robot is a promising direction of the next-generation robots. However, current control methods of musculoskeletal robots lack multi-tasks learning ability, great generalization, and biological plausibility. In this article, a motor-cortex-like recurrent neural network (RNN) and a reward modulated multi-tasks learning method are proposed. First, inspired by dynamic system hypothesis of motor cortex, the RNN is introduced to transform movement targets into muscle excitations. The condition that makes a RNN generate motor-cortex-like consistent population response is investigated. Second, a reward modulated multi-tasks learning method of such a RNN is proposed. In the experiments, the control of a musculoskeletal system is realized with multi-tasks learning ability, great generalization, and robustness for noises. Furthermore, the RNN and muscle excitations demonstrate motor-cortex-like consistent population response and human-like muscle synergies respectively. Therefore, the proposed method has better performance and biological plausibility, and verifies the neural mechanisms in the robotic research.