An expander cycle rocket engine includes secondary turbopump to further pressurize a gaseous fuel discharged from a primary turbine prior to entering the combustion chamber. The secondary turbopump is driven by fuel bled off from the primary fuel pump. A gaseous fuel that is heated from passing around the nozzle that is passed through the primary turbine to drive the primary fuel and oxidizer pumps is then passed through the secondary turbine to drive the secondary fuel compressor. With the secondary turbopump used in the Johnson-Sexton cycle engine, a thrust produced by the expander cycle rocket engine is greater than those obtained by prior art expander cycle rocket engines due to the square-cube rule.