Continual Test-time Adaptation (CTA) is a promising art to secure accuracy gains in continually-changing environments. The state-of-the-art adaptations improve out-of-distribution model accuracy via computation-efficient online test-time gradient descents but meanwhile cost about times of memory versus the inference, even if only a small portion of parameters are updated. Such high memory consumption of CTA substantially impedes wide applications of advanced CTA on memory-constrained devices. In this paper, we provide a novel solution, dubbed MECTA, to drastically improve the memory efficiency of gradient-based CTA. Our profiling shows that the major memory overhead comes from the intermediate cache for back-propagation, which scales by the batch size, channel, and layer number. Therefore, we propose to reduce batch sizes, adopt an adaptive normalization layer to maintain stable and accurate predictions, and stop the back-propagation caching heuristically. On the other hand, we prune the networks to reduce the computation and memory overheads in optimization and recover the parameters afterward to avoid forgetting. The proposed MECTA is efficient and can be seamlessly plugged into state-of-the-art CTA algorithms at negligible overhead on computation and memory. On three datasets, CIFAR10, CIFAR100, and ImageNet, MECTA improves the accuracy by at least 8.5% with constrained memory and significantly reduces the memory cots of ResNet50 on ImageNet by at least 70% without sacrificing accuracy. Our code will be published upon acceptance.