The flexural vibration stability of a coupled double-walled viscoelastic carbon nanotube conveying a fluid based on the Timoshenko beam (TB) model is investigated. The coupled system is surrounded by an elastic medium which is simulated as Pasternak foundation. Van der Waals (vdW) forces between the inner and outer CNTs are taken into account based on the Lenard-Jones model. Using small scale theories, Hamilton's principle and applying two dimensional (2D) magnetic field higher order governing equations are derived. The differential quadrature method (DQM) is applied to solve partial differential equations and investigate natural frequency of the system. The effects of viscoelastic constant, magnetic field with variable magnitudes and surface stresses on natural frequency of the structure are demonstrated in this study.