First-principles density functional calculations are performed to study the geometries, the electronic and the optical properties of AⅡAl2C4Ⅵ (A =Zn, Cd, Hg; C = S, Se) semiconductors each with a defect chalcopyrite structure. For the linear optical properties, five compounds show good transmissions of light in the IR and part of visible regions, and among them HgAl2S4 and HgAl2Se4 possess moderate birefringences. For the nonlinear optical properties, the strong second harmonic generation (SHG) response can be expected for these crystals, and the large static SHG coefficients ( 20 pm/V) are predicted in this work. The SHG response of AⅡAl2C4Ⅵ semiconductors can be attributed to the transitions from the bands near the top of valence band which are derived from S/Se p states to the unoccupied bands that are contributed by p states of Al and Hg atoms. By comparing with the optical properties of the commercialized AgGaC2 crystals, our results indicate that HgAl2S4 and HgAl2Se4 compounds are good candidates for the second-order nonlinear optical crystals in the IR region.