Verifiable Secret Sharing (VSS) has been widespread in Distributed Privacy-preserving Machine Learning (DPML), because invalid shares from malicious dealers or participants can be recognized by verifying the commitment of the received shares for honest participants. However, the consistency and the computation and communitation burden of the VSS-based DPML schemes are still two serious challenges. Although Byzantine Fault Tolerance (BFT) system has been brought to guarantee the consistency and improve the efficiency of the existing VSS-based DPML schemes recently, we explore an Adaptive Share Delay Provision (ASDP) strategy, and launch an ASDP-based Customized Model Poisoning Attack (ACuMPA) for certain participants in this paper. We theoretically analyzed why the ASDP strategy and the ACuMPA algorithm works to the existing schemes. Next, we propose an [E]fficient [By]zantine [F]ault [T]olerant-based [Ve]rifiable [S]ecret-sharing (EByFTVeS) scheme. Finally, the validity, liveness, consistency and privacy of the EByFTVeS scheme are theoretically analyzed, while the efficiency of the EByFTVeS scheme outperforms that of the-state-of-art VSS scheme according to comparative experiment results.