Finite element models (FEM) are used for estimation of the physical behavior of the structures may not accurately represent real structural responses because of inaccurate assumption of mechanical properties. For the achievement of a reliable model, the numerical responses must be adjusted to the experimental or real life responses through a proper model updating scheme. The Power Spectral Density (PSD) of the structural response subjected to a random input is opted in this research for derivation of sensitivity based model updating method. Taylor series expansion of the PSD is used to develop the sensitivity equations. Upon the consideration of all the terms of the expansion, it is possible to take advantage from an already developed method based on frequency response function (FRF). The proposed sensitivity equation has also eliminated the need for model reduction or expansion to deal with incomplete measurement which is required for most of updating methods relying on the modal data. The proposed method is examined using a numerical example to predict changes in stiffness parameters.