The implementation of the conjugate gradient (CG) method for massive MIMO detection is computationally challenging, especially for a large number of users and correlated channels. In this paper, we propose a low computational complexity CG detection from a finite-precision perspective. First, we develop a finite-precision CG (FP-CG) detection to mitigate the computational bottleneck of each CG iteration and provide the attainable accuracy, convergence, and computational complexity analysis to reveal the impact of finite-precision arithmetic. A practical heuristic is presented to select suitable precisions. Then, to further reduce the number of iterations, we propose a joint finite-precision and block-Jacobi preconditioned CG (FP-BJ-CG) detection. The corresponding performance analysis is also provided. Finally, simulation results validate the theoretical insights and demonstrate the superiority of the proposed detection.