We introduce a model for Brownian dynamics of coupled active particles in an overdamped limit. Our system consists of several identical active particles and one passive particle. Each active particle is elastically coupled to the passive particle and there is no direct coupling among the active particles. We investigate the dynamics of the system with respect to the number of active particles, viscous friction, and coupling between the active and passive particles. For this purpose, we consider an intracellular transport process as an application of our model and perform a Brownian dynamics simulation using realistic parameters for processive molecular motors such as kinesin-1. We determine an adequate energy conversion function for molecular motors and study the dynamics of intracellular transport by multiple motors. The results show that the average velocity of the coupled system is not affected by the number of active motors and that the stall force increases linearly as the number of motors increases. Our results are consistent with well-known experimental observations. We also examine the effects of coupling between the motors and the cargo, as well as of the spatial distribution of the motors around the cargo. Our model might provide a physical explanation of the cooperation among active motors in the cellular transport processes. (C) 2015 Elsevier B.V. All rights reserved.