In this paper we consider the following problem where the summation convention is used. We call the equation as porous medium equation with convection. Let u = u(x,t) be a continuous weak solution of the equation in Rn × (0 ,T] for some T> 0. Then we can establish BCP estimates and the intrinsic Harnack inequality for the solution of the equation just as the standard equation discussed by other authors previously. This work lay a main foundation of studying other properties of this problem further.