In this article, we first give the $L^{p}$ boundedness of the operator $D^{2}L^{-1}$ with BMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator $L$ with VMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition.