In today's blockchain system, designing a secure and high throughput blockchain on par with a centralized payment system is a difficult task. Sharding is one of the most worthwhile emerging technologies for improving the system throughput while maintain high security level. However, previous sharding related designs have two main limitations: Firstly, the throughput of their random-based sharding system is not high enough as they did not leverage the heterogeneity among validators. Secondly, to design an incentive mechanism to promote cooperation could incur a huge overhead on their system. In this paper, we propose RepChain, a reputation-based secure and fast blockchain system via sharding, which also provides high incentive to stimulate node cooperation. RepChain utilizes reputation to explicitly characterize the heterogeneity among the validators and lay the foundation for the incentive mechanism. We propose a new double-chain architecture which includes transaction chain and reputation chain. For transaction chain, a Raft-based synchronous consensus that can achieve high throughput has been presented. For reputation chain, the synchronous Byzantine fault tolerance that combines collective signing has been utilized to achieve a consensus on both reputation score and the related transaction blocks. It supports a high throughput transaction chain with moderate generation speed. Moreover, we propose a reputation-based sharding and leader selection scheme. To analyze the security of RepChain, we propose a recursive formula to calculate the epoch security within only O(km^2) time. Furthermore, we implement and evaluate RepChain on the Amazon Web Service platform. The results show our solution can enhance both throughout and security level of the existing sharding-based blockchain system.