1. A reliability evaluation system for a multi-state flow network that has a source node, a reception node, at least one connection node between the source node and the reception node, and a plurality of paths having a given flow upper limit from the source node, through the connection node, to the reception node, the reliability evaluation system comprising: a definition module defining each of the plurality of paths as a system state vector, each of the system state vectors having at least one grade, each of the grade having at least one element, so as to define all the elements in the j th grade of the i th system state vector as a set, wherein j is i−1; an element-gaining module comparing values of all the elements in the set, excluding the element with a greater value and other related thereof in all grades in the i th system-state vector when only one element in the set except the element with greater values so as to obtain remaining elements, or, when only one element is in the set, letting the element to be the remaining element; and a reliability calculation module using a great common factor (GCF) calculating means to calculate initial reliability based on a first system-state vector and a second system-state vector of the plurality of paths, and using the GCF calculating means to perform the calculation of the remaining element to obtain a calculation results, summing the initial reliability and the calculation results so as to obtain a reliability of the multi-state flow network.