Analytical and numerical solutions are presented for momentum and energy laminar boundary layer along a moving plate in power-law fluids utilizing a similarity transformation and shooting technique. The results indicate that for a I ratio parameter xi, the skin friction sigma decreases with the increasing in given power-law exponent n (0 < it less than or equal to I) or velocity xi or n. The shear force decreases with the increasing in dimensionless tangential velocity t, When Prandtl number N-Pr = 1, the dimensionless temperature ii (t) is a linear function of t. and the viscous boundary layer is similar to that of thermal boundary layer. In particular, w(t) = t if xi = 0 i.e.. the N velocity distribution in viscous boundary layer has the same pattern as the temperature distribution in the thermal boundary and delta = delta(T). For N-Pr greater than or equal to 1. the increase of viscous diffusion is larger than that of thermal diffusion with the increasing in N-Pr and delta(T)(t) < delta(t). The thermal diffusion ratio increases with the increasing in n (0 < n less than or equal to 1) and xi.