Motion diffusion models have recently proven successful for text-driven human motion generation. Despite their excellent generation performance, they are challenging to infer in real time due to the multi-step sampling mechanism that involves tens or hundreds of repeat function evaluation iterations. To this end, we investigate a motion latent consistency Training (MLCT) for motion generation to alleviate the computation and time consumption during iteration inference. It applies diffusion pipelines to low-dimensional motion latent spaces to mitigate the computational burden of each function evaluation. Explaining the diffusion process with probabilistic flow ordinary differential equation (PF-ODE) theory, the MLCT allows extremely few steps infer between the prior distribution to the motion latent representation distribution via maintaining consistency of the outputs over the trajectory of PF-ODE. Especially, we introduce a quantization constraint to optimize motion latent representations that are bounded, regular, and well-reconstructed compared to traditional variational constraints. Furthermore, we propose a conditional PF-ODE trajectory simulation method, which improves the conditional generation performance with minimal additional training costs. Extensive experiments on two human motion generation benchmarks show that the proposed model achieves state-of-the-art performance with less than 10\% time cost.