In order to simulate the deformation and motion of droplet at the interface between vapor and solid surface, the smoothed particle hydrodynamics method with continuum surface force model for surface tension is modified in this paper. A surface tension algorithm with boundary conditions of wall adhesion is derived using a new treatment of boundary conditions and a corrective algorithm of particle interface normal. The colours of virtual solid particles are set according to the position of fluid surface to assure that the interface normal of particles at the junction of vapor, fluid and solid phase is normal to the contact line. By introducing Brackbill's treatment of boundary conditions of wall adhesion, the interface normal between fluid particles and some virtual solid particles at the junction of vapor, fluid and solid phase is corrected. However the module of the interface normal is kept constant. Finally, based on the new algorithm, the changing process of fluid surface in a tank, wetting process of a droplet and distortion process of a droplet on solid surface driven by shear flow are simulated. The results are compared with those obtained by volume of fluid method, showing that the new method has higher accuracy and better stability, and it is adapted to deal with the engineering problems such as the deformation and motion of droplets at the interface between vapor and solid surface.