Based on the concepts of connection number and its operation rules， a connection number evaluation algorithm， by combining connection number operation with the network-equivalent method， is introduced to calculate the uncertainty reliability indices of distribution systems， of which input parameters and reliability indices can be expressed in connection numbers. In the algorithm， the connection number theory is applied to deal with various uncertainties of original parameters to calculate such connection number reliability indices in the case of certainty and/or uncertainty. Moreover， a comparison with conventional methods shows that the approach proposed is capable of reflecting the general effect of input parameter uncertainty on reliability indices and provides uncertainty information of reliability indices， which give a more refined degree of truth of system reliability. Also， the approach provides a greater amount of information and reflects the index-uncertainty more sufficiently than the methods of interval analysis and unascertained rational number. In addition， the approach has all characters of the two methods and is more useful in practice. A numerical example of IEEE RBTS indicates the rationality and effectiveness of the approach.