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Water vapour is an important substituent of the atmosphere but its spatial and temporal distribution is difficult to detect. Global Positioning System (GPS) water vapour tomography, which can sense three-dimensional water vapour distribution, has been developed as a research area in the field of GPS meteorology. In this paper, a new water vapour tomography method based on a genetic algorithm (GA) is proposed to overcome the ill-conditioned problem. The proposed approach does not need to perform matrix inversion, and it does not rely on excessive constraints, a priori information or external data. Experiments in Hong Kong under rainy and rainless conditions using this approach show that there is a serious ill-conditioned problem in the tomographic matrix by grayscale and condition numbers. Numerical results show that the average root mean square error (RMSE) and mean absolute error (MAE) for internal and external accuracy are 1.52/0.94 and 10.07/8.44 mm, respectively, with the GAMIT-estimated slant water vapour (SWV) as a reference. Comparative results of water vapour density (WVD) derived from radiosonde data reveal that the tomographic results based on GA with a total RMSE / MAE of 1.43/1.19 mm are in good agreement with that of radiosonde measurements. In comparison to the traditional least squares method, the GA can achieve a reliable tomographic result with high accuracy without the restrictions mentioned above. Furthermore, the tomographic results in a rainless scenario are better than those of a rainy scenario, and the reasons are discussed in detail in this paper. [ABSTRACT FROM AUTHOR]