Direct Numerical Simulations have been performed to study the droplet spreading behaviour on a spherical surface. A coupled immersed boundary and volume of fluid method is used to represent the gas-liquid-solid interactions. The contact area of the droplet on the surface is recorded in order to fit the initial spreading with a power-law representation, using the contact-angle and interface curvature as fitting parameters. Small viscous droplets are used to reduce interfacial oscillations as well as low drop velocities to reduce impact forces. A decrease of spreading area with increasing curvature is observed. Moreover, the model shows good agreement compared to equilibrium states. A strong contact-angle dependence is found for the pre-factor of the power law, which is expected, and a linear decrease was found in the exponent for increasing curvature of the surface.