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With the increasing expansion of power systems, random factors affecting the performance of these systems have also increased. Rising demand for electrical energy, along with the aforementioned random factors, has led to uncertainty analysis methods being of particular importance in analyzing the small signal stability of the power systems. In this paper, a method based on polynomial approximation for probabilistic small signal stability analysis of the power systems is presented. Since the correct determination of unknown coefficients has a direct effect on the accuracy of the polynomial approximation method, this paper presents a method that is able to determine these coefficients with more coverage on the probable input space of the problem and in addition, is able to maintain its efficiency even by increasing the number of random input variables. After determining unknown coefficients, the load flow results and system state matrix are determined for random changes of all loads and based on Hermit's polynomial approximation. Then, the eigenvalues ​​of the system are determined and the stability of the small signal of the system is probabilistically studied. In order to evaluate the accuracy and effectiveness of the proposed method, the IEEE 14-bus benchmark system is simulated in MATLAB software and the results of the proposed method is compared with the results of the two conventional methods of Point Estimation and Monte Carlo. Examination of the results has shown that the proposed method in this paper, in addition to validity, has good accuracy and high computational speed.