We constructe a retinal circuit model that includes cones, horizontal cells, bipolar cells, AII amacrine cells, ganglion cells and lateral geniculate nuclei, and ON and OFF pathways based on retinal anatomical structure in this paper, and introduce the STDP learning rule into the synaptic connections between layer of ganglion cells and layer of lateral geniculate nuclei. By giving a single pattern stimulus and an alternating pattern stimulus to the circuit model, respectively, we compare the corresponding results based on the firing patterns, firing frequency of spiking neurons, and the weight changes of synaptic connections with STDP learning rule, to study the characteristics of retinal circuit. We obtain several conclusions: First, the neural network can effectively convert the optical information into the pulse sequence information and show the information structural characteristics of retina. Second, the use of STDP learning rule in the final connections makes the layer of lateral geniculate nuclei learn and memorize the stimulus pattern when conducting it, and present learning independency between ON and OFF pathways. Finally, STDP learning can lead to superposition of two different pattern stimuli that appear alternately in terms of spatial distribution of synaptic connection weights, and the superposition effect of the overlap region is more obvious.