Random access is necessary in crowded scenarios due to the limitation of pilot sequences and the intermittent pattern of device activity. Nowadays, most of the related works are based on independent and identically distributed (i.i.d.) channels. However, massive multiple-input multiple-output (MIMO) channels are not always i.i.d. in realistic outdoor wireless propagation environments. In this paper, a device grouping and pilot set allocation algorithm is proposed for the uplink massive MIMO systems over spatially correlated Rayleigh fading channels. Firstly, devices are divided into multiple groups, and the channel covariance matrixes of devices within the same group are approximately orthogonal. In each group, a dedicated pilot set is assigned. Then active devices perform random pilot and data access process. The mean square error of channel estimation (MSE-CE) and the spectral efficiency of this scheme are derived, and the MSE-CE can be minimized when collision devices have non-overlapping angle of arrival (AoA) intervals. Simulation results indicate that the MSE-CE and spectral efficiency of this protocol are improved compared with the traditional scheme. The MSE-CE of the proposed scheme is close to the theoretical lower bound over a wide signal-to-noise ratio (SNR) region especially for long pilot sequence. Furthermore, the MSE-CE performance gains are significant in high SNR and strongly correlated scenarios.