In this paper, a recurrent spiking neural network model with multiple synaptic connections is constructed, and an online synaptic weight-delay learning algorithm based on spike train kernels is proposed, which can dynamically adjust both synaptic weights and delays during the learning process. A real-time error function is first constructed by applying the kernel function representation of the spike train, and then the online updating rules for synaptic weights and delays are derived by applying the gradient descent method. Spike train learning tasks and nonlinear pattern recognition tasks on UCI datasets are performed to verify the learning performance of the proposed learning algorithm. The experimental results show that the dynamic delay learning algorithm obtains higher learning accuracy in fewer learning epochs than the static delay learning algorithm, and the classification accuracy on UCI datasets is also higher than that of some common supervised learning algorithms for spiking neural networks. It can be seen that the synaptic delay plasticity and the multiple synaptic connection mode can effectively improve the learning performance of recurrent spiking neural networks.