The weighted reliability of network is defined as the sum of the multiplication of the probability of each network state by its normalized weighting factor.Under a certain state, when the capacity from source s to sink t is larger than the given required capacity C r, then the normalized weighting factor is 1, otherwise, it is the ratio of the capacity to the required capacity C r. This paper proposes a new algorithm for the weighted reliability of networks, puts forward the concept of saturated state of capacity, and suggests a recursive formula for expanding the minimal paths to be the sum of qualifying subsets. In the new algorithm, the expansions of the minimal paths dont create the irrelevant qualifying subsets, thus decreasing the unnecessary expanding calculation. Compared with the current algorithms, this algorithm has the advantage of a small amount of computations for computer implementation. The weighted reliability of network is defined as the sum of the multiplication of the probability of each network state by its normalized weighting factor. Unit a certain state, when the capacity from source s to sink t is greater than the given required capacity C r, then the normalized weighting factor is 1, otherwise, it is the ratio of the capacity to the required capacity C r. This paper proposes a new algorithm for the weighted reliability of networks, puts forward the concept of saturated state of capacity, and suggests a In the new algorithm, the expansions of the minimal paths don t create the irrelevant qualifying subsets, thus decreasing the unnecessary expanding calculation. Compared With the current algorithms, this algorithm has the advantage of a small amount of computations for computer implementation.