Local community detection aims to find a cluster of nodes by exploring a small region of the network. Local community detection methods are faster than traditional global community detection methods because their runtime does not depend on the size of the entire network. However, most existing methods do not take the higher-order connectivity patterns crucial to the network into consideration. In this paper, we develop a new Local Community Detection method based on network Motif (LCD-Motif) which incorporates the higher-order network information. LCD-Motif adopts the local expansion of a seed set to identify the local community with minimal motif conductance, representing a generalization of the conductance metric for network motifs. In contrast to PageRank-like diffusion methods, LCD-Motif finds the community by seeking a sparse vector in the span of the local spectra, such that the seeds are in its support vector. We evaluate our approach using real-world datasets across various domains and synthetic networks. The experimental results show that LCD-Motif can achieve a higher performance than state-of-the-art methods.