The effects of surface slip and heat generation (absorption) on the flow and heat transfer of a non-Newtonian power-law fluid on a continuously moving surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to nonlinear ordinary differential equations using suitable transformations. The transformed ordinary differential equations are solved numerically using the fourth order Runge–Kutta method with the shooting technique. Graphical solutions for the dimensionless velocity and the dimensionless temperature are presented and discussed for various values of the slip parameter, the heat generation or absorption parameter and the Eckert number. The results show that the local skin-friction coefficient is decreased as the slip parameter increased. Also, it is found that the local Nusselt number is decreased as the slip parameter or the heat generation parameter increased and the heat absorption parameter has the effect of increasing the local Nusselt number.