One of the challenges in the design of sparse code multiple access systems is developing low-complexity detectors. To achieve this goal, we propose a novel low-complexity detector based on an edge selection approach, which remarkably reduces the computational complexity. First, the proposed detector applies adaptive Gaussian approximation to the unselected edges that have smaller modulus of the channel coefficients, on the basis of the different channel qualities. As a result, the original factor graph can be simplified. In addition, a mean and variance feedback mechanism is employed to further compensate the information loss brought by unselected edges. Simulations show that, compared with the original message passing algorithm-based detector, the computational complexity is reduced substantially with negligible bit error rate performance degradation.