In this paper, natural convection heat transfer is numerically investigated in a square enclosure filled with power law non-Newtonian fluid model and central heat source for steady and quiet state. The top wall of the enclosure is thermally insulated and the vertical walls are at constant temperature of TC. The down wall of the enclosure also has four equal parts at constant temperature of TC and TH. The governing equations for the power-law fluid flow are solved with the numerical finite difference method based on the control volume formulation and SIMPLE algorithm. The results show that for small Rayleigh numbers the Nusselt number will not be affected by changes of the power law index but in Ra=106, thermal performance changes are more significant with the change in power law index. With a smaller the Rayleigh number in all indexs, the center of flow lines rotation, regarding to the axis parallel to axis Y, in the middle of the enclosure, will be more symmetrical. Also with stronger natural convection in the square enclosure, the average of Nusselt number for non-Newtonian fluid increase with increased power law index and improved thermal performance by increasing the Rayleigh number is impressive for the density power law fluid (n˃1). Results also show that the Rayleigh number for the start of natural convection in the square enclosure is reduced by increasing the power law index.