Generalized eigenvalue decomposition plays a vital role in statistical signal processing. Generalized decomposition aims to enhance the signal by seeking the directions that capture most of signal component but are orthogonal to the spaces constituting the noise component. Each generalized eigenvalue represents the optimal signal-to-noise ratio that can be obtained by projecting an observation into the corresponding eigen-direction. This paper proposes a generalized eigen-pairs tracking method based on conjugate gradient searching. The proposed method is variable step-size that seeks the generalized eigenvector in a sense that generalized Rayleigh quotient is optimal in the corresponding searching direction. It is suitable for extracting generalized eigenvectors from stationary and non-stationary matrix pencil. We compare the proposed method with multiple adaptive generalized extraction algorithms. The effectiveness of the proposed method is validated via numerical simulations.