Al 2 O 3 is a potential dielectric material for metal-oxide-semiconductor (MOS) devices. Al 2 O 3 films deposited on semiconductors usually exhibit amorphous due to lattice mismatch. Compared to two-dimensional graphene, MoS 2 is a typical semiconductor, therefore, it has more extensive application. The amorphousAl 2 O 3 /MoS 2 (a-Al 2 O 3 /MoS 2 ) interface has attracted people's attention because of its unique properties. In this paper, the interface behaviors of a-Al 2 O 3 /MoS 2 under non-strain and biaxial strain are investigated by first principles calculations based on density functional theory (DFT). First of all, the generation process of a-Al 2 O 3 sample is described, which is calculated by molecular dynamics and geometric optimization. Then, we introduce the band alignment method, and calculate band offset of a-Al 2 O 3 /MoS 2 interface. It is found that the valence band offset (VBO) and conduction band offset (CBO) change with the number of MoS 2 layers. The dependence of leakage current on the band offset is also illustrated. At last, the band structure of monolayer MoS 2 under biaxial strain is discussed. The biaxial strain is set in the range from -6% to 6% with the interval of 2%. Impact of the biaxial strain on the band alignment is investigated.