A new chemical looping air separation (CLAS) system, which is composed of a combined heat and power (CHP) unit and two fixed-bed reactors (FBRs), is developed for trigeneration of electricity, oxygen, and nitrogen simultaneously. Based on the specific oxidation conditions of the elevated oxidation pressure and the oxidation temperature higher than the reduction temperature, the alternate operation of two FBRs is operated periodically to avoid the solid looping cycles. Through exergy analysis of the CLAS using different oxygen carriers, the Mn-based CLAS has the lower exergy efficiency than using other oxygen carriers but it has benefits with low methane depletion rate and small reactor size. By solving a multi-objective optimization algorithm for minimizing the methane depletion rate and reactor size, the Pareto-optimal front of the Mn-based CLAS shows that the exergy efficiency improvement would increase the fuel consumption, enlarge the reactor size and reduce the feasible objective region. Through exergoeconomic analysis of the Mn-based CLAS, the specific oxidation conditions could obviously increase the exergy destruction cost of the oxidation reaction but it can be compensated by the relative cost differences of the CHP units.