The mathematical model for thermokinetic characteristics of an irreversible reciprocating Brayton cycle has been analyzed. The analytical formulas of the specific work and the actual cycle thermal efficiency are derived, taking the variable specific heats of working fluid and the irreversibility in the compressor and the turbine into account. The model mentioned above has carried on the numerical calculus under typical circulation performance parameters. The results show that the variable specific heat and the internal efficiency of both the compressor and the turbine have an obvious influence on the cycle performance, and the internal efficiency of both the compressor and the turbine have more remarkable influence on the cycle performance. The results obtained in this paper may provide a theoretical guide for the assessment and improvement of the performance of actual gas turbine engines.