In this paper, we present a novel Byzantine fault-tolerant consensus protocol for sharded blockchain networks that does not rely on expensive leader-driven communication. The proposed protocol selects a single block proposer at a time and uses threshold signatures as a voting mechanism to confirm the validity of the proposed block. By using a gossip-like communication scheme, each node can collect and recover the group signature within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {O(log}N)$ </tex-math></inline-formula> steps. With only one block proposer per consensus round, there is no possibility of conflicting blocks and resultant forks. Therefore, our consensus protocol requires only one round of one-way communication to achieve finality for each block. Our protocol guarantees safety and liveness while tolerating up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> faulty participants among <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2f+1$ </tex-math></inline-formula> nodes. Our performance study shows that the proposed protocol enables hundreds of nodes to participate in the agreement process, and can finalize large blocks in approximately 10 seconds.