Training deep learning models from a stream of nonstationary data is a critical problem to be solved to achieve general artificial intelligence. As a promising solution, the continual learning (CL) technique aims to build intelligent systems that have the plasticity to learn from new information without forgetting the previously obtained knowledge. Unfortunately, existing CL methods face two nontrivial limitations. First, when updating a model with new data, existing CL methods usually constrain the model parameters within the vicinity of the parameters optimized for old data, limiting the exploration ability of the model; second, the important strength of each parameter (used to consolidate the previously learned knowledge) is fixed and thus is suboptimal for the dynamic parameter updates. To address these limitations, we first relax the vicinity constraints with a global definition of the important strength, which allows us to explore the full parameter space. Specifically, we define the important strength as the sensitivity of the global loss function to the model parameters. Moreover, we propose adjusting the important strength adaptively to align it with the dynamic parameter updates. Through extensive experiments on popular data sets, we demonstrate that our proposed method outperforms the strong baselines by up to 24% in terms of average accuracy.