This study examines the behavior of vortex-induced vibrations in flexible nanocomposite beams by employing the lattice Boltzmann-finite element approach and taking fluid–structure interactions (FSI) into account. The lattice Boltzmann approach is deemed as fluid-field solver based on the Eulerian network; whereas, the finite element method is considered as the solid body solver based on the Lagrangian description, which is coupled to each other for the simulation of fluid–structure interaction. The multiple-relaxation times model has been utilized to enhance the accuracy of calculations at high Reynolds numbers. In addition, an improved network has been used to prevent numerical errors in areas with severe gradients. According to the Euler–Bernoulli beam technique, the nanocomposite beam is simulated and discretized based on isoparametric Hermite elements. Next, the equivalent mechanical characteristics of nanocomposite have been determined using the Halpin–Tsai model. Furthermore, the fluid model used for the Boltzmann network is a two-dimensional one. A numerical solution of the coupled differential equations is followed by an analysis of the effects of various parameters on the generated hydrodynamic force and vibration characteristics of these beams. These parameters include fluid flow rate, nanoparticle volume fraction, and geometric dimensions of the cantilever beam. Given the results, it was observed that with the increase in carbon nanotubes, the maximum amplitude of oscillations in the lock-in region decreases, in contrast to the galloping region where the presence of carbon nanotubes increases the maximum amplitude of oscillations.