The water-conveyance reliability of the large-scale reinforced concrete (RC) aqueducts is of vital importance to their functional attributes being lifeline hydraulic structures. However, on one hand, the mechanical property of concrete is equipped with remarkable randomness and nonlinearity. On the other hand, the aqueduct structures may inevitably suffer from uncertain disastrous earthquake actions during service life, posing a great threat to their service safety. To these ends, the present paper proposed a quantification framework for the water-conveyance reliability assessment of the aqueduct structures by incorporating the stochastic damage mechanics model of concrete and the probability density evolution method. The principle and implementation procedures of the developed framework were illustrated in detail on an actual large-scale RC aqueduct structure. The results show that the probability density evolution method is of high efficiency and accuracy in application to the water-conveyance reliability evaluation of aqueduct structures. The water-conveyance reliability varies with the change of pre-defined seismic fortifications, which should be reasonably accounted for in early design phases. This paper provides an important basis for the reliability analysis and optimization design of actual aqueduct structures.