Spiking Neural Network (SNN), as a brain-inspired approach, is attracting attention due to its potential to produce ultra-high-energy-efficient hardware. Competitive learning based on Spike-Timing-Dependent Plasticity (STDP) is a popular method to train an unsupervised SNN. However, previous unsupervised SNNs trained through this method are limited to a shallow network with only one learnable layer and cannot achieve satisfactory results when compared with multi-layer SNNs. In this paper, we eased this limitation by: 1)We proposed a Spiking Inception (Sp-Inception) module, inspired by the Inception module in the Artificial Neural Network (ANN) literature. This module is trained through STDP-based competitive learning and outperforms the baseline modules on learning capability, learning efficiency, and robustness. 2)We proposed a Pooling-Reshape-Activate (PRA) layer to make the Sp-Inception module stackable. 3)We stacked multiple Sp-Inception modules to construct multi-layer SNNs. Our algorithm outperforms the baseline algorithms on the hand-written digit classification task, and reaches state-of-the-art results on the MNIST dataset among the existing unsupervised SNNs.