The dynamic nature of tasks and environments in Internet of Things (IoT) systems require deep learning models to continuously retrain on evolving data to ensure their effectiveness. Existing continual learning (CL) methods aim to mitigate catastrophic forgetting, where the model loses knowledge of previous tasks when learning new ones. However, these methods often ignore the memory resource competition caused by the parallel execution of multiple applications, which limits the realworld IoT application of CL in resource-constrained edge devices. In this article, we propose EDCL, a novel approach that enhances the training efficiency and model accuracy of CL methods while ensuring the uninterrupted operation of high-priority inference programs. Specifically, we first implement a custom batch sampler that can dynamically load batches and measure the memory usage and training time recorded via offline profiling. In the online stage, by monitoring the resource consumption of high-priority programs, EDCL can dynamically select batch policies that meet resource constraints and facilitate efficient training. Additionally, we propose an adaptive hierarchical buffer swap method to enhance the model’s ability to retain previously learned knowledge and mitigate forgetting. Extensive experiments show that EDCL effectively balances training efficiency and model accuracy while preventing high-priority inference programs from failing due to memory contention, demonstrating promising performance compared to baselines.