Proof-of-work was originally proposed by Dwork and Naor in 1992 and has proved its powerfulness in Bitcoin as a decentralized mechanism for blockchain construction. Proof-of-work is the basis of most popular cryptocurrencies and smart contract systems, where participating miners are required to solve difficult mathematical problems to validate transactions. One of the major challenges that proof-of-work faces is the 51% attack, i.e., if an adversary controls more than half of the computation power, he/she can control the blockchain construction and determine which blocks will be included. This is not a major concern when the number of miners is large. However, for an early stage blockchain system with a limited number of users, it is relatively easy for an attacker to launch the 51% attack. To mitigate such risk, we propose a new hybrid blockchain construction scheme that uses the combination of proof-of-work and the stake, which is the number of coins produced by a miner, to determine whether this miner is allowed to construct a block. We prove that stakes play an important role in the hybrid scheme at the beginning, so that an attacker is not able to launch the 51% attack even if he/she controls the majority of the computational power. Meanwhile, the hybrid scheme will converge to pure proof-of-work after sufficiently many blocks are generated, and thus captures the desired properties of proof-of-work. Most importantly, such a convergence is 'smooth' in the sense that neither changes in the rules nor parameters are introduced, and thus no hard/soft-forks will be triggered. We also demonstrate the effectiveness of the new scheme using simulations with different configurations, which can help a designer to select adequate parameters for a specific blockchain application.