In this paper, a new five-branch Brayton cycle, i.e., isothermal heating modified air standard Brayton cycle, is proposed based on the isothermal heating modified steady flow Brayton cycle models established in previous literatures. The finite time thermodynamics theory is used to build the irreversible isothermal heating modified air standard Brayton cycle model. The impacts of the cycle maximum temperature ratio (τ), pre-expansion ratio (ρ) and various losses on the properties of power (P) versus compression ratio (γ), efficiency (η) versus γ, power density (Pd) versus γ, ecological function (E) versus γ, P versus η, Pd versus η and E versus η are examined. The multi-objective genetic algorithm is used to optimize different objective (η, E, P and Pd) combinations when γ is taken as the optimization variables. The deviation indexes (Ds) of the Shannon Entropy, TOPSIS and LINMAP are calculated to determine the optimal solution set. The findings demonstrate that raising ρ and τ, and lowering various losses can clearly improve cycle performance. For the optimization of P−E, the decision-making schemes of TOPSIS is better and corresponding D is 0.1342. The performance of the modified BC is better than that of the classical BC.