The thermal analysis of the annular rectangular profile fins with variable thermal properties is investigated by using the homotopy analysis method (HAM). The thermal conductivity and heat transfer coefficient are assumed to vary with a linear and power-law function of temperature, respectively. The effects of the thermal-geometric fin parameter and the thermal conductivity parameter variations on the temperature distribution and fin efficiency are investigated for different heat transfer modes. Results from the HAM are compared with numerical results of the finite difference method (FDM). It can be seen that the variation of dimensionless parameters has a significant effect on the temperature distribution and fin efficiency.