Blockchain sharding splits a blockchain into several shards where consensus is reached at the shard level rather than over the entire blockchain. It improves transaction throughput and reduces the computational resources required of individual nodes. But a derivation of trustworthy consensus within a shard becomes an issue as the longest chain based mechanisms used in conventional blockchains can no longer be used. Instead, a vote-based consensus mechanism must be employed. However, existing vote-based Byzantine fault tolerance consensus protocols do not offer sufficient security guarantees for sharded blockchains. First, when used to support consensus where only one block is allowed at a time (binary consensus), these protocols are susceptible to progress-hindering attacks (i.e., unable to reach a consensus). Second, when used to support a stronger type of consensus where multiple concurrent blocks are allowed (strong consensus), their tolerance of adversary nodes is low. This article proposes a new consensus protocol to address all these issues. We call the new protocol MWPoW+, as its basic framework is based on the existing Multiple Winners Proof of Work (MWPoW) protocol but includes new mechanisms to address the issues mentioned previously. MWPoW+ is a vote-based protocol for strong consensus, asynchronous in consensus derivation but synchronous in communication. We prove that it can tolerate up to f < n/2 adversary nodes in a n-node system as if using a binary consensus protocol and does not suffer from progress-hindering attacks.