One of the most important features of multi-tenant databases in cloud environments is scalability. However, most elastic scaling techniques struggle to make effective scaling decisions for dynamically changing loads. If load changes can be predicted in advance, resource supply can be accurately adjusted. Given this, this study proposes a load-prediction-based elastic scaling method for multi-tenant databases. It includes a combined load prediction model and an elastic scaling strategy. The load prediction model combines the advantages of convolutional neural networks, long short-term memory networks and gated recurrent units. It can accurately forecast memory requirements of database clusters. Based on the prediction results, the elastic scaling strategy adjusts the number of virtual machines to ensure that resource supply remains within a reasonable range. Compared to existing methods, the combined load prediction model can reduce prediction errors by 8.7% to 21.8% and improve prediction fitting degree by 4.6%. Furthermore, this study improves the Bayesian optimization algorithm for hyperparameter tuning of the combined prediction model. The improved hyperparameter tuning model reduces errors by above 20% and improves fitting degree by 1.04%, which proves that it can well address the poor performance of Bayesian optimization in combined domains of discrete and continuous solutions. Compared to the most widely used scaling strategy in Kubernetes, the proposed elastic scaling method reduces response time by 8.12% and latency by 9.56%. It can avoid the latency and the waste of resources to a large extent.