We present a theoretical investigation of band offsets in GaN-based group III-nitride ternary/binary heterostructures with zinc blende structure. The band offsets in InGaN/GaN and AlGaN/GaN heterostructures were studied using the recently proposed extended sp(3) tight binding model (Unlu H 2001 Phys. Status Solidi. b 223 195). Simulations show a small valence band offset in AlGaN/GaN heterostructure and large valence band offset in the InGaN/GaN heterostructure. Furthermore, the tensile strain in AlGaN leads to positive bowing of the conduction band offsets in AlGaN/GaN heterostructure, and the compressive strain in InGaN leads to negative bowing of conduction band offsets in InGaN/GaN heterostructure as a function of composition. Good agreement is found between predictions and experiment.