The influence of quantum degeneracy on the performance of a Stirling refrigeration cycle is investigated, based on the equation of state of an ideal Fermi gas. The inherent regenerative losses and the coefficient of performance (COP) of the cycle are calculated. It is found that, under the condition of strong gas degeneracy, the COP of the cycle in the first approximation is a function only of the temperatures of the heat reservoirs, while under other conditions, the COPs of the cycle depend on the temperatures of the heat reservoirs and other parameters of the cycle. The results obtained here reveal the general performance characteristics of a Stirling refrigeration cycle having a Fermi gas as its working substance.