The purpose of this research is to study the utility of prediction program like a F.E.M. analysis for energy recovery of heat exchanger with heat pipe which uses arbitrary groove wick. The program is based on the utility by the experimental and applytical method of the single heat pipe. It is also expanded and applied in the prediction program of the heat exchanger. The results are as follows; 1) The effective thermal conductivity of the groove wick with arbitrary shape is counted by the thermal resistance change. 2) The more the number of rows, the more the effect energy recovery changing by the number of rows, the bigger the free velocity, the smaller the effect of energy recovery. 3) The effect of energy recovery increases according to the value of the rate of mass flow (Me/Mc) and also number of rows. 4) The comparison between calculated and data shows good agreement within 2.5% error, therefore the F.E.M. analysis of the study is useful to predict the performance of heat pipe-heat exchanger.