Abstract: Supply-chain enterprises plays an important role in their cooperation in cloud computing, and it is the pillar of supply chain to ensure its regular operation. For the problems of without considering the importance of enterprises' recent behaviour and the time attenuation of their future behaviour, as well as without timely response for their spiteful actions in existing trust evaluation methods, an reliance quantifying and evaluation mechanism for suppliers using double sliding windows(DSW) on the basis of enterprises' behaviour is proposed. Targeting on improving the trust crisis between supply-chain enterprises, this newly-proposed mechanism take the impact of time on trust into consideration based on the time decay function. The content of window update and displacement is determined by the continuously sliding window to ensure the reliability and scalability of trust evaluation for enterprises' behaviou. The simulation experiment and analysis demonstrates that a dynamical computing of suppliers' confidence in cloud computing is provided by this model, the evaluation method could be applied in the evaluation of suppliers in cloud computing efficiently and an objective and effective result can be achieved.