BLS signature scheme is widely employed in blockchain systems due to its compact signature size and non-interactive aggregation capability. However, the standard BLS threshold signature faces critical bottlenecks. First, the verification process needs computationally expensive bilinear pairing operations. Second, the distributed key generation requires multiple communication rounds. This work introduces a novel fast-verifiable threshold BLS signature scheme. We design a non-interactive key generation protocol that integrates program obfuscation with pseudorandom functions. It enables participants to deterministically derive threshold keys for dynamic groups through a single registration, which eliminates interactive rounds. Second, we develop an efficient verification algorithm by embedding Chaum-Pedersen proofs, which bypasses the conventional bilinear pairing verification. It can shifts computational overhead to more efficient elliptic curve operations. Third, we provide formal security proofs in the random oracle model under standard cryptographic assumptions, including the co-CDH hardness assumption. It demonstrates existential unforgeability against chosen message attacks. Experimental results demonstrate that our scheme achieves over 50% faster verification compared to standard threshold BLS while preserving all essential features including signature aggregation and threshold security. The performance advantage becomes particularly pronounced in large-scale committee scenarios. The moderate overhead introduced during key generation and signing phases ensures superior overall performance in verification-intensive applications such as blockchain systems.