In a FENE bead-spring chain model,a parallel algorithm for Brownian configuration fields with finite volume method is used to simulate pressure driven pipe nows, velocity-pressure driven pipe nows with same and opposite directions. Validity of the algorithm is verified with numerical examples. Velocity,stress and stretch of molecular chain of pipe nows are obtained. It shows that the proposed algorithm overcomes shortcomings of huge computation and time-consuming for Brownian configuration fields. And it has excellent expansibility. Parallel efficiency is over 85% as number of beads is greater than two. It also shows that the time of now to reach steady state is shorter with increasing number of chain segments.