In this paper, the non-coherent transmission in grant-free massive machine-type-communication-enabled random access is studied, and a new index modulation (IM)-based non-coherent data transmission scheme is presented. In the proposed scheme, each user is allocated N (N>1) non-orthogonal pilot sequences. When the user is active, N_a (1 ≤ N_a <; N) out of the N allocated pilot sequences are activated to generate transmit signal, where the indices of these active pilot sequences are employed to carry information based on the IM principle. At receiver, first, exact and approximated presentations of the covariance matrix of received signals for the cases of N_a = 1 and N_a > 1 are derived, respectively. Then, the non-Bayesian maximum-likelihood (ML) estimator is employed to detect user activity along with embedded information bits. Finally, simulation results are given to demonstrate the performance of the proposed scheme.