High pressure, high temperature (HPHT) hydrogen mixture gas well is a well with temperature over 150o C at the bottom and require equipment working pressure of 69MPa. In this situation, a mathematical model to investigate the effect of valves on transient highpressure hydrogen-natural gas mixture production is important to producing gas industries. Many work in Natural gas producing wells were done to find lasting solutions to problems that led to the premature closure of these wells. To date, no proven solution has been accepted to cover all of the issues encountered by Natural gas producing industries especially the effect of valves closing in high- pressure hightemperature hydrogen-natural gas-producing wells. In this paper, numerical computation has been carried out on mathematical models for the transient flow of hydrogen natural gas mixture (H2NG) in a Natural gas producing well. The model consists of partial differential equations of the conservation of mass and momentum with transient conditions. A transient state occurred during operation when control valves suddenly opened and closed at the wellhead and environmental formation. The model was solved using Steger Warming Flux Vector Splitting Method. The method has been proven to be unconditionally stable and has been applied in pipeline gas transportation network. The results obtained on the flow parameter characteristics namely the pressure and temperature are presented which shows good agreement with existing work. New results of density, velocity and sound wave propagation were also presented. We conclude that the work has provide a technical reliance to gas producing industries. It will served as a way forward for solution of problems encountered during hydrogen–Natural gas production with disturbances at the wellhead and environmental formation effect in high pressure and high temperature (HPHT) gas wells.