This paper briefly reviews the history of development of ocean carbon-cycle models from the beginning of the simplest three-box model，discusses the features of various models at different times，and points out the ability of oceanic uptake of atmospheric CO₂. In recent years，the global oceancirculation model of carbon cycle often uses a simple biogeochemical model，while in the process-based model and one-dimensional model the role of ecosystem in the ocean carbon cycle is explored in relative detail. In 1995, the Ocean Carbon-Cycle Model Intercomparison Project (OCMIP) was initiated by IGBP/GAIM. Two phases have been completed. In the second phase, 13 modeling groups participated in the project. Although OCMIP is now in its third phase, some papers from the first or second phase are still in preparation. The newest global oceancirculation models estimate an annual mean oceanic uptake of 1.5-2.2 GtC of anthropogenic CO₂ for the 1980s. In spite of many achievements, which have revealed the basic features of oceanic uptake and distributions of atmospheric CO₂, many challenges still remain that require further research, which is discussed. One of serious issues is the consistency of physical fields, which can be assessed through examination of anthropogenic tracers. The parameterization of air-sea exchange of CO₂ still needs to be further studied. The use of the carbon cycle model with an explicit ecosystem is a developing trend in the study of biogeochemical cycle of carbon dioxide and its response to global change.