Using the first-principles pseudopotential plane-wave methods based on the density functional theory, the elastic constants of B2-(Ni1-xFex)Al (x=0-3.0 at%) supercells with or without Ni vacancy or Ni anti-site defect were calculated in the framework of Virtual Crystal Approximation. Several parameters, such as elastic constant C44, Cauchy pressure (C12-C44), Young modulus E, the shear modulus G and their ratio G/B0, have been adopted to characterize and assess the effect of Fe alloying concentration on the ductility and hardness of NiAl intermetallic compounds. It is found that Fe addition with x < 0.6 at% is proved to be efficient to enforce the strength or hardness of NiAl intermetallic compounds either for perfect crystals or for defect crystals. No improvement of the ductility of perfect B2-NiAl crystals can be demonstrated as Fe is added in the range from 0 to 3.0 at%. The Ni vacancy or Ni anti-site defects make the intrinsic ductility of perfect B2-NiAl crystals without Fe addition to be weakened. However, an obvious decrease in the degree of the embrittlement of B2-(Ni1-xFex)Al crystals with Ni vacancies can be seen as Fe alloying concentration x is lower than 0.5 at%, and the optimum additions locate in the range from 0.2 at% to 0.4 at%. From these calculations, a deduction therefore is conduced. That is for the distinct increase in the elongation rate of a B2-NiAl single crystal with Fe addition of 0.20-0.25 at% in the experiments could originate from the correlative and cooperative effects between vacancies and Fe addition in the B2-NiAl crystal