In order to engineer the strength of an exchange bias in a cubic Heusler alloy layer, crystalline strain has been induced at a ferromagnet/antiferromagnet interface by their lattice mismatch in addition to the conventional interfacial exchange coupling between them. Such interfaces have been formed in (Co2FeAl0.5Si0.5(CFAS)/Cr)3 structures grown by ultrahigh vacuum molecular beam epitaxy. The magnetic and structural properties have been characterised to investigate the exchange interactions at the CFAS/Cr interfaces. Due to the interfacial lattice mismatch of 1.4%, the maximum offset of 18 Oe in a magnetisation curve has been measured for the case of a CFAS (2 nm)/Cr (0.9 nm) interface at 193 K. The half-metallic property of CFAS has been observed to remain unchanged, which agrees with the theoretical prediction by Culbert et al (2008 J. Appl. Phys. 103 07D707). Such a strain-induced exchange bias may provide insight of the interfacial interactions and may offer a wide flexibility in spintronic device design.