The climate system is composed of five spheres in the earth system, i.e., atmosphere, hydrosphere, cryosphere, lithosphere and biosphere. The interaction among these spheres of climate system determines the natural climate variability. As the human activities increase, more and more influence has exerted on the climate system. Both natural and anthropogenic climate changes have influenced greatly on the society, the economics and the human life, and have led to the arousing of the issues on the national security, the environmental diplomacy and the sustainable development, etc. In order to understand the climate change and its forcings, and forecast the future climate change, the basic need is to set up a comprehensive climate observing system dealing with the five spheres in the earth system. The detailed information on the variation of the climate system can be provided by the high quality climate data and related products obtained from the climate observing system. The development of designing a climate observing system in China is reviewed, especially the role played by the Chinese Academy of Meteorological Sciences. Based on the analysis of the climate observing system, some crucial issues concerning the setting up of the climate observing system are discussed. These issues include the scientific requirements to the climate observing system, its representativeness, comprehensiveness, standard, supportiveness to the climate prediction and projection and to the climate model development, application to the interdisciplinary, social and economical application, data opening and sharing, assimilation and reanalysis of the climate system data, and the rescue of the historical data.