The method of Brownian configuration fields (BCF) is a promising multi-scale approach for the simulationof viscoelastic fluids, however, it is a computationally expensive method, which restricts its application in complex scenarios. Therefore, it is of great importance to optimize the parallel implementation in order to improve computational efficiency. In this paper we propose a hybrid decomposition parallel algorithm named: MCDPar, whichenables the simulation problem to bedecomposed simultaneously over mesh cells andthe Brownian configuration fields. Compution processes are split into multiple groups and Brownian configuration fields are equally associated with these groups. Meanwhile, within each group the processes are concurrently executed based on the traditional mesh decomposition approach. Finally we implemented the MCDPar algorithm in a micro-macro numerical solver based on OpenFOAM. Experimental results show that the micro-macro simulation time of viscoelastic fluids issignificantly reduced with improved scalability and parallel efficiency. In the test case with Nf = 2000 and Ncell = 262144, the speedup of the MCDParis up to 9.23x with a 7.5x increase in number of cores compared to the original parallel algorithm.