In this paper, a numerical model is developed for direct simulation of droplet impinging onto a spherical surface on a fixed Eulerian mesh. The model couples the level-set method and the interfacial cell immersed boundary method to the single-fluid formulation of the Navier-Stokes equations which are solved by a finite-volume projection technique. Moving contact lines are modelled here with a simple static contact angle model. The model is shown to converge, and to agree with previous work in the literature. The model is then applied to investigate the impact behaviour of a droplet onto solid sphere of different diameters at low Weber number and low Reynolds number. The simulation results show that the droplet used in present study seems to deposit on different spherical surfaces through oscillating. The simulated results also suggest that the impacted-sphere size has a significant effect on the impact dynamics of the droplet. A local breakage phenomenon may be found in the centre of the droplet collision with a smaller sphere during the first recoiling stage. A regime map is then established to provide quantitative analysis for the breakage mode of the current impacting process.