Sub-synchronous oscillation （SSO） has always been a widely concerned stability issue in power systems. Currently, there are multiple methods for analyzing SSO, such as eigenvalue analysis method and frequency-domain analysis method （such as impedance analysis method）, but each method has its own advantages and disadvantages. Combing the advantages of frequency-domain analysis easy to quantify and eigenvalue analysis methods easy to model, a new method for directly estimating the SSO eigenvalues is proposed based on the admittance frequency response characteristics. The method can directly estimate the SSO eigenvalues based solely on the extreme features （including extreme point frequency and slope information） of the frequency response curves of the system aggregated admittance and admittance integral, making the calculation simple and fast. The effectiveness of the proposed method is verified by comparing it with the results of eigenvalue analysis tool in MATLAB. The method is suitable for quantitative analysis of different types of SSO, such as sub-synchronous torsional oscillation in the conventional power generation, sub/super-synchronous oscillation in the renewable energy generation, and composite sub-synchronous oscillation in the conventional and renewable energy power bundling delivery. The analysis results have all been verified by PSCAD/EMTDC simulation.