In this paper we present a reconstruction method for the determination of small unknown mass attached to a nanobeam resonator. The method uses as data the resonant frequency shifts produced by the added mass in an initially uniform nanobeam under longitudinal vibration and under clamped boundary conditions. The support of the mass variation is assumed to be contained in half of the axis interval and a simplified strain gradient theory in linear elasticity is used to take into account the size effects. The reconstruction is based on a sequence of linearizations of the inverse eigenvalue problem in a neighborhood of the initial beam. Numerical simulations show that the identification method performs well, even for not necessarily small mass changes.