The mammalian olfactory system uses odor-specified temporal codes to represent the quality and the quantity of different odors. In order to better understand this coding strategy, a biologically plausible spiking neural network (SNN) was built and evaluated. In this study, MNIST images of handwritten digits were used to mimic the two-dimensional representation of odor information by the glomeruli in the olfactory bulb. The images were used to train the SNN based on the spike-timing-dependent plasticity (STDP) unsupervised learning rule. The SNN model was implemented by Izhikevich neurons to represent both the pyramidal neurons and the GABAergic interneurons in the piriform cortex. The recognition accuracy of the SNN model was evaluated to gain insights for the temporal coding scheme in the olfactory system. The results suggested that the SNN model can effectively encode 2D neural representations with temporal codes and achieved discrimination accuracies close to animal behavioral performances in odor discrimination tasks.