Index modulation multiple access (IM-MA) is recently proposed to exploit the IM concept to the uplink multiple access system, where multiple users transmit their own signals via the selected time slots. However, the computational complexity of the optimal maximum-likelihood (ML) detection in IM-MA is tremendously high when the number of users or time slots is large. In this letter, we propose a low-complexity detection method for IM-MA, which is inspired by the log likelihood ratio (LLR) algorithm. In addition, because of the heavy search burden for all LLR values, we further propose a suboptimal method to determine the permutation set, which records the number of users allocated to each time slot. Simulation results and the complexity analysis verify that the proposed detection performs closely to the optimal ML detection with reduced computational complexity.