A fundamental double-stage Rankine cycle system using the single-component working fluid in each stage for liquefied natural gas (LNG) cold exergy recovery is used as a base case in the present paper. An advanced scheme of three-stage Rankine cycle system with the cooling output part is then proposed and designed. A series of cases are simulated within the fundamental and the advanced system schemes by employing the single-component working fluid and binary or ternary mixture working fluids. To settle the optimization problem of the poly-stage system with the multi-component working fluids, the priority-oriented composition optimization is performed based on the Genetic Algorithm in the advanced three-stage system. The thermal efficiencies, the exergy efficiencies and the exergy analysis are conducted in all the cases. As a result, the performances of the thermal and exergy efficiencies rise from 3.5% and 7.16% in the initial case to 17.33% and 25.7% in the fully optimized case respectively. The heat transfer analysis and the parameter study of the pump outlet pressure of the working fluids in the advanced three-stage Rankine cycle system are presented. Furthermore, the economic analysis is conducted as well to evaluate the novel cryogenic Rankine power system for future engineering design.