Federated learning (FL) has shown great potential for addressing the challenge of isolated data islands while preserving data privacy. It allows artificial intelligence (AI) models to be trained on locally stored data in a distributed manner. In order to build an ecosystem for FL to operate in a sustainable manner, it has to be economically attractive to data owners. This gives rise to the problem of FL incentive mechanism design, which aims to find the optimal organizational and payment structure for the federation in order to achieve a series of economic objectives. In this paper, we present a VCG-based FL incentive mechanism, named FVCG, specifically designed for incentivizing data owners to contribute all their data and truthfully report their costs in FL settings. It maximizes the social surplus and minimizes unfairness of the federation. We provide an implementation of FVCG with neural networks and theoretic proofs on its performance bounds. Extensive numerical experiment results demonstrated the effectiveness and economic reasonableness of FVCG.