Ultrawide-bandgap semiconductor heterojunctions Sc 2 O 3 / GaN and θ-Al 2 O 3 /GaN are explored in the framework of density functional theory (DFT). The dielectric-dependent hybrid (DDH) functional, which is superior to other semilocal hybrid functionals in describing the dielectric screening that is dominant in wide-bandgap materials, is adopted in this study. The calculated band gaps of GaN, Sc 2 O 3 , and θ-Al 2 O 3 can be well matched to the existing experimental measurements. Both Sc 2 O 3 /GaN and θ-Al 2 O 3 /GaN heterojunctions present type-I band alignments, and the valence/conduction band offsets of the Sc 2 O 3 /GaN and θ-Al 2 O 3 /GaN heterojunctions exhibit the values of 0.93/1.89 and 2.25/0.95 eV, respectively. The computational methods and procedures could be used to predict the band offsets of other wide-bandgap semiconductor heterojunctions.