This paper investigates the performance of interleave division multiple access (IDMA)-based random access with various interference canceller structures in order to support massive machine-type communications (mMTC) in the fifth generation (5G) mobile communication system. To support massive connectivity in the uplink, a grant-free and contention-based multiple access scheme is essential to reduce the control signaling overhead and transmission latency. To suppress the packet loss due to collision and to achieve multi-packet reception, non-orthogonal multiple access (NOMA) with interference cancellation at the base station receiver is essential. We use IDMA and compare various interference canceller structures such as the parallel interference canceller (PIC), successive interference canceller (SIC), and their hybrid from the viewpoints of the error rate and decoding delay time. Based on extensive computer simulations, we show that IDMA-based random access is a promising scheme for supporting mMTC and the PIC-SIC hybrid achieves a good tradeoff between the error rate and decoding delay time.