PageRank has been widely used to measure the authority or the influence of a user in social networks. However, conventional PageRank only makes use of edge-based relations, which represent first-order relations between two connected nodes. It ignores higher-order relations that may exist between nodes. In this paper, we propose a novel framework, motif-based PageRank (MPR), to incorporate higher-order relations into the conventional PageRank computation. Motifs are subgraphs consisting of a small number of nodes. We use motifs to capture higher-order relations between nodes in a network and introduce two methods, one linear and one non-linear, to combine PageRank with higher-order relations. We conduct extensive experiments on three real-world networks, namely, DBLP, Epinions, and Ciao. We study different types of motifs, including 3-node simple and anchor motifs, 4-node and 5-node motifs. Besides using single motif, we also run MPR with ensemble of multiple motifs. We also design a learning task to evaluate the abilities of authority prediction with motif-based features. All experimental results demonstrate that MPR can significantly improve the performance of user ranking in social networks compared to the baseline methods.