The present article is majorly arranged to survey the vibration problem of a nanocomposite beam reinforced by graphene oxide powder (GOP) whenever the structure is subjected to a nonuniform magnetic field. A higher-order trigonometric refined beam model is extended to achieve the governing equation of the problem according to Hamilton's principle. The effect of a nonuniform magnetic field is applied to the governing equations by combining the magnetic induction relations of Maxwell with the displacement field equations. Then, the achieved equations are solved by implementing Galerkin's method to consider the influence of different boundary conditions on the vibrational responses of the beam. On the other hand, the accuracy and efficiency of the presented model is verified by comparing the results from this work with that of published researches. Finally, effects of different variables on the dimensionless frequency of GOP reinforced composite beams are highlighted in the framework of tables and diagrams.