Abstract: To analyze the dynamic stability for a cantilevered single-walled carbon nanotube (SWCNT) conveying magnetic-fluid flow embedded in double-parameter foundation under longitudinal magnetic field, the governing equations of motion and boundary conditions were obtained based on the magnetohydrodynamics and nonlocal Euler-Bernoulli beam model. Applying the differential quadrature method (DQM), the vibration differential equation was solved. The effects of the nonlocal parameter, magnetic field, magnetic-fluid flow and the parameters of elastic foundation on vibration of carbon nanotube were discussed. The numerical calculation results indicate that as the external magnetic field and elastic foundation parameters increase, the critical instability flow velocity of the system increases, and the dynamic stability of the system is enhanced. However, the nonlocal parameter increases, the critical instability flow velocity decreases, and the dynamic stability of the system weakens. It is particularly important that compared to the case of conveying non-magnetic fluid, the carbon nanotube conveying magnetic fluid will be more stable under the magnetic field.