The method of nonlocal maximum principle was initiated by Kiselev et al (Inve. Math. 167 (2007), 445-453), and later developed by Kiselev (Adv. Math. 227 no. 5 (2011), 1806-1826) and other works. The general idea is to show that the evolution of considered equation preserves a suitable modulus of continuity, so that one gets the uniform-in-time control on the solution. In this talk, by using the method of nonlocal maximum principle and introducing some new moduli of continuity, we consider a class of drift-diffusion equations with nonlocal Levy-type diffusion, and we prove the eventual regularity result in the supercritical type cases, where the eventual regularity time can be evaluated small as the supercritical index approaching to the critical index for fixed initial data. We also show the global regularity of the vanishing viscosity solution in the logarithmically supercritical case. The talk is based on joint work with Changxing Miao from IAPCM, China.