The rising penetration of renewable generation as a result of environmental concerns generates increased uncertainties in power systems. This necessitates probabilistic analyses of the system performance, which include probabilistic power flow (PPF). The PPF suffers from the curse of dimensionality due to a large number of random loads. To address this issue, a multivariate dimension-reduction (MDR) method is proposed for PPF studies in this paper. The MDR decomposes the PPF problem into lower dimensional PPF subproblems which are further solved with promising accuracy. The computation time of the proposed method is proportional to the number of wind farms, which noticeably facilitates computation. The proposed method is applied to the IEEE 118-bus system and 2383-bus system. Simulation results demonstrate the accuracy and effectiveness of the proposed method.