Abstract: Neutron noise is the stochastic fluctuation of the neutron field under the influence of various weak perturbations, attracting attention as an indirect monitoring tool for nuclear reactors. This paper establishes a frequency-domain numerical simulation method for neutron noise based on the unstructured-grid variational nodal method using the first-order perturbation theory and Fourier transform techniques. This work extends the functionality of the general-purpose neutron transport code VITAS. The accuracy of the frequency-domain method is verified by comparing its results with those from time-domain methods in the MOX case and the C4V benchmark. Numerical results indicate that the frequency-domain method can achieve a precision comparable to the existing time-domain method under weak perturbations. The relative error in the amplitude of neutron noise is less than 2%, and the relative error in the phase of neutron noise is less than 1%.