For the coordinated multipoint (CoMP) transmission in Long-Term Evolution (LTE) systems, its performance is greatly impacted by the estimation of timing offsets (TOs) between cell-edge user equipment (UE) and transmit points, which is supposed to be dealt with by using the random access (RA) procedure. Available RA schemes for the CoMP transmission offer poor RA performance in terms of multiuser detection, TO estimation, power estimation, and access delays. To improve the RA performance and fully exploit the CoMP structure, in this paper, we propose a novel centralized parallel RA (CP-RA) scheme, which performs in threefold. First, a novel RA subchannel allocation scheme is proposed to suppress mutual interference between coordinated users and noncoordinated users. Second, an iterative parallel interference cancelation (IPIC)-based multiuser detection and estimation algorithm is proposed on the basis of the space-alternating generalized expectation–maximization (SAGE) algorithm. Finally, the coordinated diversity of the system structure could be exploited to implement centralized multiuser detection. Analyses and simulation results show that the proposed RA scheme is able to provide satisfied RA performance compared with existing schemes.