In this paper, the impact of imperfect channel state information (CSI) on a downlink coordinated multipoint (CoMP) transmission system with non-orthogonal multiple access (NOMA) is investigated since perfect knowledge of a channel cannot be guaranteed in practice. Furthermore, the channel estimation error is applied to estimate the channel information wherein its a priori of variance is assumed to be known. The impact of the number of coordinated base stations (BSs) on downlink CoMP NOMA is investigated. Users are classified into one of two groups according to their position within the cell, namely, cell-center user (CCU) and cell-edge user (CEU). In this paper, ergodic capacity and sum capacity for both CCU and CEU are derived as closed forms. In addition, various experiments are conducted with different parameters such as SNR, error variance, and power allocation to show their impact on the CoMP method. The results show that CoMP NOMA outperforms the CoMP orthogonal multiple access (OMA) wherein the condition of the channel impacts the performance of CoMP NOMA less. It is worth noting that a higher number of coordinated BSs enhances the total capacity of CoMP NOMA. Finally, the performance analysis is validated due to the close accordance between the analytical and simulation results.