Neumann series (NS) expansion-based precoder in massive multiple input multiple output systems suffers from slow convergence. To solve this problem, this letter proposes a weighted NS expansion precoder. The weights are designed to minimize the error between the exact inverse and the weighted NS inverse. The optimal weights are deduced analytically. Moreover, an approximation of these optimal weights is proposed, based on the properties of large Wishart matrices, which saves the re-computation of these weights. The weighted NS precoding provides near optimal performance at only four weighted expanded NS terms and has lower complexity than recently proposed approximate precoders.