Reliability of the natural gas pipeline network is related to security of gas supply directly. According to the different required functions of the natural gas pipeline network, its reliability is divided into three aspects, namely mechanical reliability, hydraulic reliability, and gas supply reliability. However, most of the previous studies confused the definitions of the hydraulic reliability and gas supply reliability. Moreover, the uncertainty in the process of supplying natural gas to the targeted market and the hydraulic characteristic of the natural gas pipeline network are often ignored. Therefore, a methodology to assess hydraulic reliability and gas supply reliability of the natural gas pipeline network is developed in the study, and the uncertainty and hydraulic characteristic of the natural gas pipeline network are both considered. The methodology consists of four parts: establishment of the indicator system, calculation of the gas supply, prediction of the market demand, and assessment of the hydraulic reliability and gas supply reliability. Moreover, a case study is applied to confirm the feasibility of the methodology, and the reliability evaluation results provide a comprehensive picture about the abilities of the natural gas pipeline network to perform the specified gas supply function and satisfy consumers' demand, respectively. Furthermore, a comparison between these two types of reliability is presented. The results indicate that the natural gas pipeline network may not be able to meet the market demand even if the system completes the required gas supply tasks due to the impact of the market demand uncertainty.