Abstract: According to Taylor expansion, boundary layer equations for the power-law fluids with variable thermal conductivity along a horizontal wavy surface are reduced in detail.The energy equation with variable thermal conductivity is constructed, where heat conduction coefficient is power-law function dependent on temperature gradient. A series of transformations are introduced to transform the original wavy surface to a system of partial differential equations, which is solved numerically by the Keller-box method. The effects of the wavy amplitude-wavelength ratio, power-law indexand generalized Prandtl numberon the local friction coefficient and heat transfer coefficient are discussed. The local Nusselt number and the friction coefficient will vary like wave-shape periodically though there is a sudden change near the zero point. Furthermore, both of them will decrease with increasing wavelength ratio. With the increasing magnitude, the oscillation also will increase. With the increasing power-law index, the local Nusselt number will decrease.