We present a theoretical study of the valence-band offsets (VBOs) of the pseudomorphic Si1-x-yGexCy/Si(001) heterojunctions. Our calculation is based on the ab initio pseudopotential method, the virtual-crystal approximation, and the average-bond-energy theory. It is found that the VBO is sensitive to the strain condition. Initial addition of carbon increases the VBO of the relaxed Si12x2yGexCy/Si(001) heterostructures. For constant Ge fraction, the VBO decreases and increases with increasing the C fraction in the case of the compressive and tensile strains, respectively. The trends of our results are in agreement with those of other theoretical and experimental results.