Many papers have described heat transfer in a regenerator core. We tried to obtain an approximate solution of original partial differential equations dealing with heat transfer between gas and core. The exact solution of the original equations is so complicated that the equations were converted to simultaneous ordinary differential equations by using the finite difference form. We obtained the approximate solution described here and inspected it for accuracy. We then applied it to evaluation of the heat transfer rate of a model core. This method was compared to max. slope method, and the precision of the calculated results was verified.