In the massive multiple-input and multiple-output (Massive MIMO) systems, the maximum likelihood (ML) detection problem is NP-hard and becoming classically intricate with the number of transmitting antennas and symbols increasing. The quantum approximate optimization algorithm (QAOA), a leading candidate algorithm running in the noisy intermediate-scale quantum (NISQ) devices, can show quantum advantage for approximately solving combinatorial optimization problems. In this paper, we propose the QAOA based on the maximum likelihood detection solver of binary symbols. In the proposed scheme, we first conduct a universal and compact analytical expression for the expectation value of the 1-level QAOA. Second, a Bayesian optimization based parameters initialization is presented, which can speedup the convergence of the QAOA to a lower local minimum and improve the probability of measuring the exact solution. Compared to the state-of-the-art QAOA based ML detection algorithm, our scheme has the more universal and compact expectation value expression of the 1-level QAOA, and requires few quantum resources and has the higher probability to obtain the exact solution.