The colour temperature and the correlated colour temperature are important parameters of the sources. Because of the complex calculation process between the colour temperature, the correlated colour temperature and the chromatic coordinate (u,v), it is difficult to analyze the expression of uncertainty according to the international organization for standardization (ISO) guide. Based on the ISO guide to the expression of uncertainty, correlated colour temperature uncertainty is derived from the analytical equation between the chromatic coordinate (u,v) and the colour temperature. Accurate analytical method, approximate calculation, geometrical projection method and traditional method are discussed and compared, which are used to evaluate the uncertainty of the new national secondary standard of colour temperature at National Institute of Metrology (NIM). Traditional uncertainty analysis is mostly based on experimental statistic and experience estimation, and no mathematical relation is found between the colour temperature uncertainty and the spectral irradiance values. The analytical methods described in this paper are more accurate and reasonable.