We investigate a non-linear precoding techniques for multi-user multiple-input multiple-output (MU-MIMO) downlink. When assuming full knowledge of the channel state information at the transmitter, a vector perturbation (VP) is a promising precoding scheme that approaches sum capacity and has simple receiver. However, its encoding is nondeterministic polynomial time (NP)-hard problem. In the MU-MIMO downlink, this encoding problem becomes harder because the proper user selection must be considered. In this paper, we propose a new vector perturbation scheme based on eigenvalue normalization (VPEVN), which converts the NP-hard problem into a channel condition-based finite integer problem, resulting in a reduction of encoding complexity. In addition, it can select a good user set by simple maximum norm criterion owing to its orthogonalization effect.