Risk assessment of dam's running status is an important part of dam management. A data-driven method based on monitored displacement data has been applied in risk assessment, owing to its easy operation and real-time analysis. However, previous data-driven methods considered displacement data series at each monitoring point as an independent variable and assessed the running status of each monitoring point separately, without considering the correlation between displacement of different monitoring points. In addition, previous studies assessed the dam's running status qualitatively, without quantifying the risk probability. To solve the above two issues, a displacement-data driven method based on a multivariate copula function is proposed in this paper. Multivariate copula functions can construct a joint distribution which reveals the relevance structure of random variables. We assumed that the risk probability of each dam section is independent and took monitoring points at one dam section as examples. Starting from the risk assessment of single monitoring points, we calculated the residual between the monitored displacement data and the modelled data estimated by the statistical model, and built a risk ratio function based on the residual. Then, using the multivariate copula function, we obtained a combined risk ratio of multi-monitoring points which took the correlation between each monitoring point into account. Finally, a case study was provided. The proposed method not only quantitatively assessed the probability of the real-time dam risk but also considered the correlation between the displacement data of different monitoring points.