In this letter we propose a new method to estimate the covariance matrix under the constraint that its off-diagonal elements are non-negative, which has applications to portfolio selection in finance. We incorporate the non-negativity constraint in the maximum likelihood (ML) estimation problem and propose an algorithm based on the block coordinate descent method to solve for the ML estimate. To study the effectiveness of the proposed algorithm, we perform numerical simulations on both synthetic and real-world financial data, and show that our proposed method has better performance than that of a state-of-the-art method.