Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the structure and inherent properties of the network. Most existing network embedding methods didn't consider network noise. However, it is almost impossible to observe the actual structure of a real-world network without noise.  The noise in the network will affect the performance of network embedding dramatically. In this paper, we aim to exploit node similarity to address the problem of social network embedding with noise and propose a node similarity preserving (NSP) embedding method. NSP exploits a comprehensive similarity index to quantify the authenticity of the observed network structure. Then we propose an algorithm to construct a correction matrix to reduce the influence of noise. Finally, an objective function for accurate network embedding is proposed and an efficient algorithm to solve the optimization problem is provided. Extensive experimental results on a variety of applications of real-world networks with noise show the superior performance of the proposed method over the state-of-the-art methods.