A new method using three dimensions of cloud continuity, including range dimension, Doppler dimension, and time dimension, is proposed to discriminate cloud from noise and detect more weak cloud signals in vertically pointing millimeter-wave cloud radar observations by fully utilizing the spatiotemporal continuum of clouds. A modified noise level estimation method based on the Hildebrand and Sekhon algorithm is used for more accurate noise level estimation, which is critical for weak signals. The detection method consists of three steps. The first two steps are performed at the Doppler power spectrum stage, while the third step is performed at the base data stage. In the first step, a new adaptive spatial filter combined with the Kuwaraha filter and the Gaussian filter, using the ratio of mean to standard deviation as the adaptive parameter, is applied to initially mask the potential cloud signals to improve the detection performance at the boundary of cloud and noise. Simulations of boundary cases were performed to compare our adaptive filter and normal Gaussian filters. Box filters are used in steps two and three to remove the remaining noise. We applied our method to cloud radar observations with TJ-II cloud radar at the Nanjing University of Information Science & Technology. The results showed that our method can detect more weak cloud signals than the usual methods, which are performed only at the Doppler power spectrum stage or the base data stage.