Focused on the issue that the traditional fingerprint matching methods based on minutiae are mainly applicable for large-size fingerprint and the accuracy rate would reduce significantly when dealing with small-size fingerprint from smart phone, a small-size fingerprint matching method based on deep learning was proposed. Firstly, the detailed information of minutiae was extracted from fingerprint images. Secondly, the Regions Of Interest (ROI) were searched and labeled based on minutiae. Then a lightweight deep neural network was built and improved from original residual module. In addition, binary feature pattern and triplet loss were used to optimize and train the proposed model respectively. Finally, the small-size fingerprint matching was accomplished with the fusion strategy of registration and matching. The experimental results show that the Equal Error Rate (EER) of the proposed method can reach 0.50% and 0.58% on public FVC_DB1 and in-house database respectively, which is much lower than the traditional fingerprint matching methods based on minutiae, and can improve the performance of small-size fingerprint matching effectively and meet the requirements on smart phone.