Quantum key distribution (QKD) can help distant agents to share unconditional secret keys, andthe achievable secret key rate can be enhanced with the help of decoy-state protocol. To implementQKD experimentally, the agents are supposed to accurately transmit a number of different intensitypulses with the LiNbO3 based Mach-Zehnder (LNMZ) intensity modulator. However, the bias driftof LNMZ intensity modulator may affect the performance of a QKD system. In this letter, we reveala simple RC circuit model to demonstrate the bias drift in the LNMZ intensity modulator. Andbased on the model, we propose a multi-step bias stable scheme to control the bias working point.Experimental result shows that our scheme can eliminate the bias drift of at arbitrary working pointwithin a long time range. Besides, there is no need of any feedback mechanisms in the scheme. Thismeans our scheme will not lead to any increasement in system complexity, making it more suitablefor a QKD system.