One of the important features of multi-tenant databases in cloud environments is scalability. However, most elastic scaling techniques struggle to make effective scaling decisions for complex workload variations. If workload changes can be predicted in advance, resources can be accurately adjusted. In this paper, we propose a memory load-based elastic scaling method for multi-tenant databases, including a cluster-level load prediction model and an elastic scaling strategy. The load prediction model integrates the advantages of convolutional neural networks, long short-term memory networks, and gated recurrent units to accurately forecast the memory load requirements of the database cluster. The elastic scaling strategy, based on the demand prediction results, precisely adjusts the number of virtual machines to ensure that resource provisioning remains within a reasonable range. Compared to existing methods, this model reduces prediction errors by 8.7% to 21.8% and improves prediction fitting by 4.6%. Additionally, this paper improves the Bayesian optimization algorithm for hyperparameter tuning of this model. It addresses the issue of poor performance of Bayesian optimization in combined domains of discrete and continuous solutions, further reducing errors by 7.6% and improving fitting by 1.04%. Experimental results indicate that compared to the most widely used scaling strategy in Kubernetes, the elastic scaling method proposed in this paper avoids the latency and resource waste associated with elastic scaling. Response time is reduced by 8.12%, latency by 9.56%.