Our investigation centers on the issue of linear precoding for hybrid-ARQ retransmissions in linear multi-input-multi-output (MIMO) channels driven by non-Gaussian inputs. Leveraging recent works on single transmission MIMO precoding , we derive the gradient of input-output mutual information with respect to precoder matrix for optimization. We further establish that the right eigenvectors of optimum precoder are determined by the associated minimum mean-square error (MMSE) matrix. We then propose a gradient algorithm for maximizing the mutual information. Compared with precoders designed for Gaussian input, our new precoders can significantly improve the input-output mutual information, especially at low signal-to-noise ratio (SNR) and for lower dimensional constellations.