In this paper, we propose a low-complexity symbol detection algorithm for massive multiple-input multiple-output (MIMO) uplink. Grounded on the fact that a primary property of the massive MIMO systems guarantees the convergence of the Jacobi method, the method is exploited in the linear detection so that the estimate of transmitted symbols can be obtained without employing the computationally intensive matrix inversion. In addition, we propose a multiplication-free initial estimate for the Jacobi method in order to lessen the computational complexity further. Owing to the elimination of matrix inversion and the efficient initial estimate, the proposed algorithm achieves near-optimal error-rate performance with fewer computations than the state-of-the-art schemes.