In this study, analytical solutions are presented for the unsteady electroosmotic flow of linear viscoelastic fluid between micro-parallel plates. The linear viscoelastic fluid used here is described by the general Jeffrey model. Using Laplace transform method, the solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Jeffrey constitutive equation. By numerical computations, the influences of the dimensionless relaxation time λ1 and retardation time λ2 on velocity profile are presented. In addition, we find that when the retardation time is zero, the smaller the relaxation time, the more close to the Newtonian fluid velocity profile the velocity profile is. With the increases of the relaxation time and the retardation time, the velocity amplitude also becomes bigger and bigger. As time goes by, the velocity tends to be stable gradually.