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. (C) 2017 Elsevier Ltd. All rights reserved.