We propose a modified supervised learning algorithm for optical spiking neural networks, which introduces synaptic time-delay plasticity on the basis of traditional weight training. Delay learning is combined with the remote supervised method that is incorporated with photonic spike-timing-dependent plasticity. A spike sequence learning task implemented via the proposed algorithm is found to have better performance than via the traditional weight-based method. Moreover, the proposed algorithm is also applied to two benchmark data sets for classification. In a simple network structure with only a few optical neurons, the classification accuracy based on the delay-weight learning algorithm is significantly improved compared with weight-based learning. The introduction of delay adjusting improves the learning efficiency and performance of the algorithm, which is helpful for photonic neuromorphic computing and is also important specifically for understanding information processing in the biological brain.