The deep spiking neural network (DSNN) model contains a mass of parameters, a high-performance deep model depends on a huge quantity of labeled data for solving specific problems, but collecting these labeled data is time-consuming and costly. Semi-supervised learning methods can overcome these difficulties by the unlabeled and labeled data. This paper proposes a semi-supervised multi-spike learning algorithm for DSNNs, in which the unsupervised learning rule based on spike timing-dependent plasticity is applied to adjust the synaptic weights through the unlabeled data, and the supervised learning rule based on broadcast alignment mechanism is applied to update the network weights through the labeled data. Applying spike train to encode image data, the proposed algorithm is validated on the MNIST digital image benchmark dataset. Compared with supervised learning using the labeled data, experiments indicate that the comparable classification accuracy can be achieved by the proposed semi-supervised method in DSNNs.