Temporal network embedding, which aims to learn the low-dimensional representations of nodes in temporal networks that can capture and preserve the network structure and evolution pattern, has attracted much attention from the scientific community. However, existing methods suffer from two main disadvantages: 1) they cannot preserve the node temporal proximity that capture important properties of the network structure; and 2) they cannot represent the nonlinear structure of temporal networks. In this paper, we propose a high-order nonlinear information preserving (HNIP) embedding method to address these issues. Specifically, we define three orders of temporal proximities by exploring network historical information with a time exponential decay model to quantify the temporal proximity between nodes. Then, we propose a novel deep guided auto-encoder to capture the highly nonlinear structure. Meanwhile, the training set of the guide auto-encoder is generated by the temporal random walk (TRW) algorithm. By training the proposed deep guided auto-encoder with a specific mini-batch stochastic gradient descent algorithm, HNIP can efficiently preserves the temporal proximities and highly nonlinear structure of temporal networks. Experimental results on four real-world networks demonstrate the effectiveness of the proposed method.