Meteorological cloud platforms (MCP) are gradually replacing the traditional meteorological information systems to provide information analysis services such as weather forecasting, disaster warning, and scientific research. However, the explosive growth of meteorological data resources has brought new challenges to the placement and management of big data in MCP. On the one hand, managers of MCP need to save energy to achieve cost savings. On the other hand, users need shorter data access time to improve user's experience. Hence, a big data placement method in MCP is proposed in this paper to deal with challenges above. First, the resource utilization, the data access time, and the energy consumption in MCP with the fat-tree topology are analyzed. Then, a corresponding data placement method, using the improved non-dominated sorting genetic algorithm III (NSGA-III), is designed to optimize the resource usage, energy saving, and efficient data access. Finally, extensive experimental evaluations validate the efficiency and effectiveness of our proposed method.