Multidimensional resource allocation is a hot topic in cloud computing, but current cloud platforms support only fixed resource allocation, that is, the user resource requirements are consistent throughout the usage period, which may cause a waste of resources and reduce the revenue of resource providers. Therefore, time-varying multidimensional resource allocation and the corresponding pricing mechanism represent a new challenge in cloud computing. We address the problem of online time-varying multidimensional resource allocation and pricing in clouds. Specifically, (1) we propose a novel integer programming model for the time-varying multidimensional resource allocation problem and (2) we design a truthful online auction mechanism for resource allocation in a competitive environment. For the resource allocation algorithm, we propose a waiting period strategy and dominant-resource-based strategy to improve the social welfare and resource utilization. Simultaneously, a payment pricing algorithm based on critical value theory is proposed. Finally, we prove that the mechanism is truthful and individual rationality. Compared with existing research, our approach is characterized by high social welfare, high resource utilization and short execution time.