In this work, the dynamical collision process between two miscible/immiscible micro-droplets is simulated by a modified smoothed particle hydrodynamics (C-SPH) method. In order to improve the numerical accuracy and stability of traditional SPH method, a kernel gradient modified scheme without kernel derivative is considered. Meanwhile, an improved surface tension technique based on the van der Waals model is adopted to deal with the moving interface. The reliability of C-SPH method of simulating the deformation process between two droplet collisions is tested through the numerical simulations of coalescence process between two miscible Newtonian droplet collisions. Subsequently, the coalescence process of miscible polymer droplet collision and the deformation process of bouncing and separation between two immiscible droplet collisions are investigated, in which the control equations of droplets are all based on the van der Waals model. The influences of the collision velocity, collision angle and the density ratio on the deformation process of collision are discussed, and the changes of liquid bridge and rotation angle are analyzed.