This paper concerns the regularity criteria of the three-dimensional magnetohydrodynamic (MHD) system in anisotropic Lebesgue spaces. Two regularity results were proved under additional assumptions on the horizontal components of the velocity field $\mathbf{u}$ and the magnetic field $\mathbf{B}$, or directions of Elsässer's variables $\mathbf{u}\pm \mathbf{B}$.