Deep recurrent spiking neural networks (DRSNNs) are stacked with the recurrent spiking neural machine (RSNM) modules. However, because of their intricately discontinuous and complex recurrent structures, it is difficult to pre-training the synaptic weights of RSNMs by simple and effective learning method in deep recurrent network. This paper proposed a new unsupervised multi-spike learning rule and the RSNM is trained by this rule, the complex spatiotemporal pattern of spike trains are learned. The spike signal will complete the two processes of forward propagation and reverse reconstruction, and then adjust the synaptic weight according to the error. This algorithm is successfully applied to spike trains, the learning rate and neuron number in the RSNMs are analyzed. In addition, the layer-wise pre-training method of DRSNN is presented, and the reconstruction error shows the algorithm has a better learning effect.