With the emergence of various social networks, the social media network data is analyzed from the perspective of variety by more and more researchers. The data fusion of multiple social networks relies on user identification across social networks. Concerning the low utilization problem of heterogeneous relation between social networks of the traditional Friend Relationship-based User Identification (FRUI) algorithm, a new Weighted Hypergraph based User Identification (WHUI) algorithm across social networks was proposed. Firstly, the weighted hypergraph was accurately constructed on the friend relation networks to describe the friend relation and the heterogeneous relation in the same network, which improved the accuracy of presenting topological environment of nodes. Then, on the basis of the constructed weighted hypergraph, the cross network similarity between nodes was defined according to the consistency of nodes' topological environment in different networks. Finally, the user pair with the highest cross network similarity was chosen to match each time by combining with the iterative matching algorithm, while two-way authentication and result pruning were added to ensure the recognition accuracy. The experiments were carried out in the DBLP cooperation networks and real social networks. The experimental results show that, compared with the existing FRUI algorithm, the average precision, recall, F of the proposed algorithm is respectively improved by 5.5 percentage points, 3.4 percentage points, 4.6 percentage points in the real social networks. The WHUI algorithm can effectively improve the precision and recall of user identification in practical applications by utilizing only network topology information.