Currently, the hardware design of spiking neural networks based on digital circuits has a low synaptic parallel nature in terms of learning function, leading to a large overall hardware delay, which limits the speed of online learning of spiking neural network models to some extent. To address the above problems, this paper proposed an efficient spiking neural network online learning hardware architecture based on FPGA parallel acceleration, which accelerates the training and inference process of the model through the dual parallel design of neurons and synapses. Firstly, a synaptic structure with parallel spike delivery function and parallel spike time-dependent plasticity learning function was designed; then, the learning layers of input encoding layer and winner-take-all structure were built, and the implementation of lateral inhibition of the winner-take-all network was optimized, forming an impulsive neural network model with a scale of 784~400. The experiments show, the hardware has a training speed of 1.61 ms/image and an energy consumption of about 3.18 mJ/image for the SNN model and an inference speed of 1.19 ms/image and an energy consumption of about 2.37 mJ/image on the MNIST dataset, with an accuracy rate of 87.51%. Based on the hardware framework designed in this paper, the synaptic parallel structure can improve the training speed by more than 38%, and reduce the hardware energy consumption by about 24.1%, which can help to promote the development of edge intelligent computing devices and technologies.