This study addresses the long delay issue in underwater wireless sensor networks (UWSNs) caused by the spatio-temporal complexity and dynamics of the underwater environment, which significantly impacts the information propagation between mobile sensor nodes and consequently leads to large node localization errors. To this end, a novel underwater mobile node localization algorithm based on CNN-LSTM sound speed prediction is proposed. Initially, the sound speed dataset is partitioned using the K-fold cross-validation method. Subsequently, a hybrid CNN-LSTM model is constructed and trained, leveraging the feature extraction capability of CNN and the sequence modeling strength of LSTM. This model efficiently captures both spatial and temporal information from the sound speed dataset, thereby enhancing the prediction accuracy. During the localization process, the predicted sound speed values from the CNN-LSTM model are employed for time difference of arrival (TDOA) ranging, and the ranging values are refined accordingly. Finally, the refined ranging values are utilized to adaptively select the optimal ranging and localization method for unknown nodes under varying node densities, based on the number of reference nodes, thereby achieving precise localization of underwater mobile nodes. Experimental results demonstrate that, compared to existing localization algorithms such as SLMP, DMP, NDSMP, and BLSM, the proposed MCLS localization algorithm reduces the mean localization error by 46.96%, 39.93%, 27.64%, and 15.24%, respectively, under the same beacon node conditions, significantly improving the localization accuracy and stability of underwater mobile nodes.