The potential energy surface of the HBr-N2O (1:1) cluster was calculated as a function of the inter-molecular distance and two angle variables using an ab initio method. We find that all possible structures in the circumference on the potential surface converge to two stable geometric isomers, namely, the N-end linear type (BrH-N2O) and the O-end bent type (N2O-HBr). The conversion barrier between the two stable isomers is found to be 6.3 kJ/mol at the equilibrium geometries, which is regarded to be high enough to discriminate the two stable structures even at preparation temperature of the general cluster beam experiment.