The aim of this paper is to study the effects of a magnetic field on unsteady flow of a viscoelastic fluid with the fractional Burgers' model between two parallel plates .The fractional calculus approach is introduced to establish the constitutive relationship of the viscoelastic fluid. Closed form solutions for velocity and shear stress are obtained by using the finite Fourier sine transform and discrete Laplace transform of the sequential fractional derivatives. For ==1 the solution that are obtained are going corresponding to ordinary Oldroyd-B fluid. Finally, the effect of the material parameters on the velocity profile and shear stress profile spotlighted by means of the graphical illustrations.