A geometrically asymmetric trapezoidal fin with variable fin base thickness and height is optimized based on the fixed fin base height using a one-dimensional analytic method. The temperature profile along the normalized X position in the fin is presented. For the fixed fin base height, the optimum heat loss, fin length and efficiency as a function of inside fluid convection characteristic number, fin base thickness and height, fin shape factor, convection characteristic numbers ratio and ambient convection characteristic number are represented. One of the results shows that the effect of fin base height and ambient convection characteristic number on the optimum values is remarkable.