Single crystals of CuGaSe ₂ were studied using magnetophotoluminescence in magnetic fields up to 20 T at 4.2 K. The rate of the diamagnetic shift in the A free exciton peak was determined to be 9.82×10^-6 eV / T ² . This rate was used to calculate the reduced mass as 0.115m₀ , the binding energy as 12.9 meV, the Bohr radius as 5.1 nm and an effective hole mass of 0.64m₀ ( m₀ is the free electron mass) of the free A exciton using a low-field perturbation approach and the hydrogenic model.