Brain-inspired models have become a focus in artificial intelligence field. As a biologically plausible network, the recurrent neural network in reservoir computing framework has been proposed as a popular model of cortical computation because of its complicated dynamics and highly recurrent connections. To train this network, unlike adjusting only readout weights in liquid computing theory or changing only internal recurrent weights, inspired by global modulation of human emotions on cognition and motion control, we introduce a novel reward-modulated Hebbian learning rule to train the network by adjusting not only the internal recurrent weights but also the input connected weights and readout weights together, with solely delayed, phasic rewards. Experiment results show that the proposed method can train a recurrent neural network in near-chaotic regime to complete the motion control and working-memory tasks with higher accuracy and learning efficiency.