The establishment and thermal stability of exchange bias between the ferromagnetic NiFe layer and antiferromagnetic FeMn layer have been studied. We focused on the relationship between FeMn grain size and exchange bias with the size of FeMn grains controlled by varying Cr content in Ni-Fe-Cr alloy buffer layer. The results indicate that, smaller FeMn grains lead to a larger exchange bias field, but the thickness with the exchange bias setting on is larger, which is consistent with Mauri's model. Thermal stability of the exchange bias indicates that, the films with bigger FeMn grains have a higher blocking temperature, which is in agreement with Noshioka's conclusion: bigger antiferromagnetic grains possess higher activation energies and longer relaxation times.