In this research, we propose an enhanced Grey Wolf Optimizer (GWO) for designing the evolving Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM) networks for time series analysis. To overcome the probability of stagnation at local optima and a slow convergence rate of the classical GWO algorithm, the newly proposed variant incorporates four distinctive search mechanisms. They comprise a nonlinear exploration scheme for dynamic search territory adjustment, a chaotic leadership dispatching strategy among the dominant wolves, a rectified spiral local exploitation action, as well as probability distribution-based leader enhancement. The evolving CNN-LSTM models are subsequently devised using the proposed GWO variant, where the network topology and learning hyperparameters are optimized for time series prediction and classification tasks. Evaluated using a number of benchmark problems, the proposed GWO-optimized CNN-LSTM models produce statistically significant results over those from several classical search methods and advanced GWO and Particle Swarm Optimization variants. Comparing with the baseline methods, the CNN-LSTM networks devised by the proposed GWO variant offer better representational capacities to not only capture the vital feature interactions, but also encapsulate the sophisticated dependencies in complex temporal contexts for undertaking time-series tasks.