An attempt has been made to obtain two respective universal equations, applying to different regions, elevations and seasons in the world, for remote sensing the atmospheric precipitable water vapor (Q) and the path-integrated cloud liquid water content (L) by using a ground-based dual-frequency (20.6 and 31.4 GHz) microwave radiometer (GBDFMR). To do so, a set of a priori radiosonde data with a total of 2742 cases was selected in typical seasons (winter and summer) at eight radiosonde stations (Beijing, Guangzhou, Guam, Yap, Lhasa, Zhangye, Nagqu and Lijiang) typical of the climates of mid-latitude mainland, tropical marine, plain, plateau and mountain, respectively. A cloud model was constructed in a way much the same as that by Decker et al. (1978, pp. 1789-1790) and an ensemble of cloudy- and clear-day mixed samples were elaborately constructed. Based on this ensemble, numerical simulation was done for each case by using a microwave radiation transfer model to compute the radiometric brightness temperatures T-b1 and T-b2 as well as the dependent variables L and Q. The simulated T-b1 and T-b2 together with surface air temperature, surface humidity, surface pressure, the index of clear or cloudy day, cloud base height and their combinations were used as the candidates for the predictors of multivariate regression. The stepwise regression and ridge regression techniques ensure the two respective resultant regression equations to be steady, optimal and feasible for retrieval of L and Q. The tests on these equations by using temporal and spatial extrapolation samples with total of 1020 cases show that they have quite good accuracies for predicting the Q and L and can be used operationally. This work suggests a broad prospect in the application of GBDFMR in cloud liquid water and precipitable water vapor measurements.