An estimation of daily suspended sediment concentration (SSC) is required for water resource and environmental management. The traditional methods for simulating daily SSC focus on modeling the SSCs themselves, whereas the cross-correlation structure between SSC and streamflow has received only minor attention. To address this issue, we propose a stochastic method to generate long-term daily SSC using multivariate copula functions that account for temporal and cross dependences in daily SSCs. We use the conditional copula method to construct daily multivariate distributions to alleviate the complications and workload of parameter estimations using high-dimensional copulas. The observed daily streamflow and SSC data are normalized using the normal quantile transform method to relax the computationally intensive model of building daily marginal distributions. Daily SSCs can thus be simulated through the multivariate conditional distribution using previous daily SSC and concurrent daily streamflow values. The proposed method is rigorously examined by application to a case study at the Pingshan station in the Jinsha River Basin, China, and compared with the bivariate copula method. The results show that the proposed method has a high degree of accuracy, in preserving the statistics and temporal correlation of daily SSC observations, and better preserves the lag-0 cross correlation compared with the bivariate copula method. The multivariate copula framework proposed here can accurately and efficiently generate long-term daily SSC data for water resource and environmental management, which play a critical role in accurately estimating the frequency and magnitude of extreme SSC events.