In order to improve distribution system reliability evaluation efficiency with original parameter uncertainty taken into consideration, a method based on multiple scenarios technique and blind number is proposed. Firstly, the change process of reliability parameters on distribution system component is analyzed and the method to obtain the initial blind intervals and credibility by bathtub-shaped curve function is proposed. In order to reduce the complexity of the reliability assessment, the backward scenarios reduction technique is utilized to cut down the degree of blind number scenarios, with which a minimum scenario is used to fit reliability parameters uncertainty to the maximum extent. Finally, a new algorithm of reliability assessment is proposed, of which the sequential hierarchy matrix is used to transfer the impact of element block faults on the downstream load reliability indexes while the reverse hierarchy matrix is used to transfer the impact of disconnector block faults on upstream load reliability indexes. The reliability assessment results of the example show that the algorithm is effective and feasible. This work is supported by the Specialized Research Fund for Doctoral Program of Higher Education of China (No. 20110141110032).