We study the existence of traveling wave front solutions for a three species competition system with discrete space (lattice dynamical system) or continuous space(partial differential equations). First, we study the lattice dynamical system and show that there exists a positive constant (the minimal wave speed) such that a traveling front exists if and only if its speed is above this constant. Applying the results of the lattice dynamical system and the discrete Fourier transform, we then show the existence of traveling wave solutions for the continuous model. Also, the linear determinacy for the minimal speed is addressed.