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In the framework of the generalized Lorenz–Mie theory (GLMT), the optical force and torque on a graphene-coated gold nanosphere by a vector Bessel beam are investigated. The core of the particle is gold, whose dielectric function is given by the Drude–Sommerfeld model, and the coating is multilayer graphene with layer number <i>N</i>, whose dielectric function is described by the Lorentz–Drude model. The axial optical force <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>F</mi><mi>z</mi></msub></semantics></math></inline-formula> and torque <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>z</mi></msub></semantics></math></inline-formula> are numerically analyzed, and the effects of the layer number <i>N</i>, wavelength <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>, and beam parameters (half-cone angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mn>0</mn></msub></semantics></math></inline-formula>, polarization, and order <i>l</i>) are mainly discussed. Numerical results show that the optical force and torque peaks can be adjusted by increasing the thickness of the graphene coating, and can not be adjusted by changing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mn>0</mn></msub></semantics></math></inline-formula> and <i>l</i>. However, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mn>0</mn></msub></semantics></math></inline-formula> and <i>l</i> can change the magnitude of the optical force and torque. The numerical results have potential applications involving the trapped graphene-coated gold nanosphere.