The non-isothermal Johnson-Mehl-Avrami (JMA) equation has been often used to represent phase transformation behavior in many systems involving nucleation and growth. However, the JMA equation contains three unknown parameters, i.e., the activation energy (Q), pre-exponential factor (k0 and JMA exponent (n). At present there is no unified method to assign the values of these important parameters. Earlier studies used graphical technique for estimating the values of n and k0 assuming a fixed value of Q. Since the transformation rate is very sensitive to the values of all three JMA parameters, none of these parameters can be assumed to be known. The goal of the present work is to estimate all three parameters of the JMA equation through an inverse modeling approach. The approach involves a combination of numerical thermo-fluid calculations, JMA equation for nucleation and growth for non-isothermal systems, and genetic algorithm (GA) as the optimization tool that utilizes a limited volume of experimental kinetic data for ferrite to austenite transformation in the heat affected zone (HAZ) of gas tungsten arc (GTA) welded 1005 steel. The austenite phase fractions computed by using the optimized JMA parameters showed the best agreement to date with the corresponding experimental results.