An attempt is made to extend the General Differential Quadrature Rule (GDQR) to the analysis for flowinduced vibration of curved pipes conveying. Based on the equation of in-plane vibration of curved pipes conveying fluid, the GDQR is applied to discretize the pipe modal, leading to a set of equations for the fluidconveying pipes' dynamic behaviour. Calculations of natural frequencies and critical fluid velocities by GDQR show reasonably agreement with the analytical solutions. Further, this paper investigates the typical dynamic responses of a clampedclamped curved pipe conveying fluid. As a result, the represented research shows that the GDQR can deal with these curved pipe models easily with satisfactory computation precision. Therefore, the application of GDQR for nonlinear vibrations of pipes conveying fluid will be the subject of further study.