Abstract: The impulse Poiseuille flow of generalized second grade fluid was discussed in this paper. Combining the Riemann-Liouville fractional constitutive equation of second grade fluid with the fractional momentum equation of incompressible fluid,a new governing equation was established. The velocity analytical solution was obtained based on the Fourier sine transform and the fractional Laplace transform. The numerical simulation was performed by Stehfest algorithm method. The influences of various relevant parameters such as fractional derivative parameters and retardation time were elucidated through graphs. The results show that the velocity overshoot phenomenon mainly depends on the time fractional parameter of the momentum equation.