In this paper, a kernel gradient corrected smoothed particle hydrodynamics (KGC-SPH) method is proposed to simulate the deformation process of a viscous liquid drop. The KGC-SPH method has higher accuracy and better stability than the SPH method, which is verified by simulating the stretching and rotating process of an isothermal viscous liquid drop, and the property of preservation of total angular momentum of the present method is also checked. And then, the formation of a stable spherical liquid drop based on van der Waals model is investigated, and a phenomenon of periodic oscillation with small amplitude is observed. Meanwhile, a new variable smoothing length is presented to remove the unstable phenomenon and a new surface tension technique is adopted in the simulation. Subsequently, the phenomenon of periodic oscillation of a van der Waals model liquid drop is simulated using KGC-SPH method, in which the influence of the elongation and Reynolds number on the amplitude and oscillation period is discussed.