The effect of variable viscosity on the free-convection boundary layer over a permeable vertical cone in a porous medium saturated with non-Newtonian power-law fluid has been studied numerically. The governing equations describing the problem are transformed into a system of nonlinear ordinary differential equations by using a similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the power-law index, blowing/suction parameter and the viscosity parameter on the temperature profiles and the local Nusselt number are discussed.