This paper presents a three-dimensional thirteen-velocity (D3Q13) multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for incompressible flows. The model can eliminate the second kind of compressibility error existing in previous D3Q13 MRT LB models. We simulate the three-dimensional steady Poiseuille flow, unsteady pulsatile flow, and lid-driven cavity flow to verify the validity of the current model. The excellent agreement between the numerical result and the analytical solution or the previous numerical result demonstrates the model's effectiveness.