This paper addresses issues related to the development of a computational theory and corresponding methods for studying complex socioeconomic systems. We propose a novel computational framework called ACP (Artificial societies, Computational experiments, and Parallel systems), targeting at creating an effective computational theory and developing a systematic methodological framework for socioeconomic studies. The basic idea behind the ACP approach is: 1) to model the complex socioeconomic systems as artificial societies using agent techniques in a "bottom-up” fashion; 2) to utilize innovative computing technologies and make computers as experimental laboratories for investigating socioeconomic problems; and 3) to achieve an effective management and control of the focal complex socioeconomic system through parallel executions between artificial and actual socioeconomic systems. An ACP-based experimental platform called MacroEconSim has been discussed, which can be used for modeling, analyzing, and experimenting on macroeconomic systems. A case study on economic inflation is also presented to illustrate the key research areas and algorithms integrated in this platform.