For the coordinated multipoint (CoMP) transmission in LTE systems, its performance is greatly impacted by the estimation of timing offsets (TOs) between cell-edge user equipments 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 work, we propose a novel centralized parallel RA scheme, which performs in threefold. Firstly, a novel RA sub-channel allocation scheme is proposed to suppress mutual interference between coordinated users and non-coordinated users. Secondly, an iterative parallel interference cancellation based multiuser detection and estimation algorithm is proposed on the basis of the space alternating generalized expectation-maximization 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 to existing ones.Index Terms-long term evolution, coordinated multipoint, centralized parallel random access, frequency division multiplexed sub-channels, iterative parallel interference cancellation, coordinated diversity.