There were very limited modeling studies are around a phase change material based double-spiral coiled heat exchanger, due to the difficulties of model development and the lack of mature simulation tools. When a phase change material based double-spiral coiled heat exchanger applied in an air source heat pump for defrosting, its model development becomes more complicated. To solve this fundamental problem, a mathematical model for such heat exchanger was developed, as well as the numerical solution method proposed. To improve the convergence and the speed of numerical simulation of the phase change material's heat transfer process, both of special treatments in space and time were conducted. According to the circular shape boundary, an implicit solution method was used to reduce the number of grids so that computation became convenient. Heat storage and release processes of this model were finally experimentally validated in a specially built heat pump system during frosting and defrosting, respectively. The deviation conditions are demonstrated acceptable with the mean average temperature differences at the small range of -0.71-1.64 degrees C. Potential uses and limitations of the modeling work are also further discussed. Contribution of this work are meaningful for the optimization of heat pump and any other systems, where applied a phase change material based heat exchanger.