This letter investigates linear precoding scheme that maximizes the mutual information (MI) of multiple-input multiple-output (MIMO) channel with arbitrary input constellations. Since traditional precoding schemes which rely on the relationship between MI and minimum mean-square error (MMSE) are too time consuming, this letter first proposes a lower bound of MI with which the computational complexity can be significantly reduced compared with direct computation of MI, and we prove that the bound is asymptotically optimal with a constant shift. Based on this lower bound, a low-complexity precoding scheme is obtained. Numerical results verify the effectiveness and high-performance of the proposed precoding method compared with traditional precoding schemes.