We report on the direct growth and characterization of type-II InAs/GaSb superlattice (T2SL) MWIR photodetector structure grown on a GaAs substrate by molecular beam epitaxy. The designed photodetector structure contains 140 period of 8.0 ML InAs/8.3 ML GaSb p-i-n SL structure with a 50% cutoff wavelength of 3.78 pm. We achieved a peak specific detectivity (D*) and differential resistance area product at zero bias (R(0)A) of 1.3 x 10(12)cm Hz(1/2) W-1 and 10(4) Omega cm(2) at 80 K, respectively. The obtained D* value is the best value reported up to now for a T2SL MWIR p-i-n photodetector grown on a GaAs substrate. The crystalline quality and the uniformity of the grown structure were verified by high resolution X-ray diffraction method by measuring three different spots on grown structure on a full 4 inch SI GaAs substrate.