To predict hydraulic transients of operating processes of control valve of LO₂ delivery pipes for space vehicle, mathematical models of rigid pipe, corrugated pipe, LO₂ tank and control valve were established on consideration of the influences of unsteady friction and corrugated pipe elastic deformation, numerical computation was carried out by method of characteristics to solve first order partial differential equation and method of linear theory to solve second order non-linear equation with single variable. Different influence to transient flow is discussed by changing flow characteristic, motion index and motion time of control valve. Calculations show that pressure surge in transient flow caused by operation of valve with equal percentage flow characteristic (VWEPFC) is significantly weaker than that of valve with quick opening flow characteristic(VWQOFC). The total accuracy of LO₂ delivery is more easily controlled on operation of VWEPFC opposite to VWQOFC. Extending the closing time of VWEPFC could reduce the pressure surge efficiently, but the effect of extending the closing time of VWQOFC is mainly delayed arrival time rather than reduction of water hammer wave. Valve motion index of VWEPFC equal 1.0 and fast-opening along with slow-closing program is optimum to transient control of LO₂ delivery pipes. 