This paper mainly studies the solute dispersion driven by the periodic oscillatory electro-osmotic flow of viscoelastic fluid described by Maxwell constitutive modeling. Series expansion and transform methods are used to solve the unsteady convection dispersion equation. Analytic expressions of the natural dispersion coefficient K(t) and the mean concentration C-m are derived. By numerical computation, the influences of several nondimensional parameters, such as electrokinetic width K oscillating angular frequency to of the external forced electrical field, oscillating Reynolds number Re and relaxation time De on the dispersion coefficient K(t) and mean concentration Cm are investigated. The augment in amplitude of K(t) and quick decrease of C-m reflect the enhancement of the mass transfer process. Results indicate that smaller K and omega lead to larger amplitude of K(t) and quicker reduction of C-m. Moreover, the increase in De also can magnify the amplitude of K(t) and decrease the mean concentration Cm. In addition, we find there exists a critical oscillating Reynold number Re by analyzing the variations of K(t) and Cm with Re. Finally, comparing to the case of Newtonian fluid by setting De = 0, a more effective dispersion process for Maxwell fluid can be observed interestingly. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries. (C) 2017 Elsevier Ltd. All rights reserved.