Developers often search and reuse existing code snippets in the process of software development. Code search aims to retrieve relevant code snippets from a codebase according to natural language queries entered by the developer. Up to now, researchers have already proposed information retrieval (IR) based methods and deep learning (DL) based methods. The IR-based methods focus on lexical matching, that is to rank codes by relevance between queries and code snippets, while DL-based methods focus on capturing the semantic correlations. However, the existing methods rarely consider capturing two matching signals simultaneously. Therefore, in this paper, we propose CSRS, a code search model with relevance matching and semantic matching. CSRS comprises (1) an embedding module containing convolution kernels of different sizes which can extract n-gram embeddings of queries and codes, (2) a relevance matching module that measures lexical matching signals, and (3) a co-attention based semantic matching module to capture the semantic correlation. We train and evaluate CSRS on a dataset with 18.22M and 10k code snippets. The experimental results demonstrate that CSRS achieves an MRR of 0.614, which outperforms two state-of-the-art models DeepCS and CARLCS-CNN by 33.77% and 18.53% respectively. In addition, we also conducted several experiments to prove the effectiveness of each component of CSRS.