PURPOSE: To improve reliability by forming a gas cooler for a stirling engine in such constitution that stress by inner pressure thereof is reduced.

CONSTITUTION: Recessed grooves 13, 14 which are respectively communicated with the cooling water inlet 11 and -outlet 12 of a heat exchanger head 10 and being formed extending over the whole of cooling water groove 4 of a gas cooler main body 1, are provided on the inner surface of the heat exchanger head 10 so as to make efficiently flow cooling water in the outer circumferential cooling water groove 4 of the gas cooler main body 1 which is fit in the heat exchanger head 10 having the cooling water inlet 11 and outlet 12, and prevent the wall thickness of the gas cooler main body 1 from thinning.