Conventional spin-transfer torque-based magnetoresistive random access memory (STT-MRAM) with CoFeB electrodes has great potential as universal memory. However, state-of-the-art STT-MRAM technology has encountered the issues such as high writing current density and low thermal stability for scaling down to 1x nm. Heusler alloy has been suggested as an alternative to resolve these problems by significantly reducing the Gilbert damping constant while preserving approximately 100% spin polarization. In particular, L2(1)-ordered Co2FeAl (CFA)-based magnetic tunnel junction (MTJ) exhibits outstanding half-metallicity and perpendicular magnetorcystalline anisotropy characteristics arising from Co(Fe)-O orbital hybridization at the interface. In this work, we investigate the biaxial strain effects of CFA-based MTJ by adjusting in-plane lattice constants from -4% to +4%. Our density functional theory - nonequilibrium Green's function (DFT-NEGF) calculations present that FeAl-O interfaced MTJ shows a converged tunneling magnetoresistance (TMR) ratio under compressive strain while Co-2-O interfaced MTJ shows strain-sensitive TMR ratio under both compressive and tensile strain. The difference in the current-density trends for the two types of MTJs is mainly attributed to the additional state arising from Fe-O bonding. Our results emphasize the careful control of straintronic techniques on CFA-MTJs.