A novel grant-free random access scheme with a high success rate is proposed to support massive access for machine-to-machine communications in massive multiple-input–multiple-output (MIMO) systems. This scheme allows active user equipments (UEs) to transmit their modulated uplink messages and super pilots consisting of multiple subpilots to a base station (BS). Then, the BS performs channel state information (CSI) estimation and uplink message decoding by utilizing a proposed graph combined clustering independent component analysis (GCICA) decoding algorithm and then employs the estimated CSIs to detect active UEs by using the characteristic of asymptotic favorable propagation of massive MIMO channel. We call this proposed scheme as the GCICA-based random access (GCICA-RA) scheme. We analyze the successful access probability, missed detection probability, and uplink throughput of the GCICA-RA scheme. Numerical results show that the GCICA-RA scheme significantly improves the successful access probability and uplink throughput, decreases missed detection probability, and provides low CSI estimation error at the same time.