Two slip effects, Brownian diffusion and thermophoresis, on flow, heat, and mass transfer of an incompressible viscous nanofluid over a stretching horizontal cylinder in the presence of suction/injection are discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases and found to be in a good agreement.