GeSn alloys have recently emerged as complementary metal–oxide–semiconductor (CMOS)-compatible materials for optoelectronic applications. Although various photonic devices based on GeSn thin films have been developed, low-dimensional GeSn quantum structures with improved efficiencies hold great promise for optoelectronic applications. This study theoretically analyses Ge-capped GeSn pyramid quantum dots (QDs) on Ge substrates to explore their potential for such applications. Theoretical models are presented to calculate the effects of the Sn content and the sizes of the GeSn QDs on the strain distributions caused by lattice mismatch, the band structures, transition energies, wavefunctions of confined electrons and holes, and transition probabilities. The bandgap energies of the GeSn QDs decrease with the increasing Sn content, leading to higher band offsets and improved carrier confinement, in addition to electron–hole wavefunction overlap. The GeSn QDs on the Ge substrate provide crucial type–I alignment, but with a limited band offset, thereby decreasing carrier confinement. However, the GeSn QDs on the Ge substrate show a direct bandgap at higher Sn compositions and exhibit a ground-state transition energy of ~0.8 eV, rendering this system suitable for applications in the telecommunication window (1550 nm). These results provide important insights into the practical feasibility of GeSn QD systems for optoelectronic applications.