We study the Brownian motion of a single ellipsoidal particle diffusing in a narrow channel by video-microscopy measurement. The experiments allow us to obtain the trajectories of ellipsoids and measure the diffusion coefficients. It is found that the channel constraints lead to suppression of the particle motion, especially the perpendicular motion to the channel, and the long axis of the particle tends to be parallel to the channel. A stable stratification phenomenon is observed, which is rarely discussed in studies of spherical particles. We also derive an approximate solution of theoretical prediction with the method of reflections, and obtain numerical simulation results using finite element software. They are proven to be effective by comparing them with the experimental results. All of these indicate that the aspect ratio and size of ellipsoid, the width of channel, and the transverse position distinctly affect the Brownian motion of ellipsoids.