Abstract: A hammering test is an experimental modal analysis method widely used in academia and industry. The spectral estimation method is usually used to calculate the frequency response function (FRF), which is extremely susceptible to length and quality of the measurement data. In recent years, the Bayesian learning technology has provided a new exploration approach for the system and the control field. Inspired by this, the prior information of the FRF is statistically described by a complex Gaussian process, and a Bayesian inference method is developed for estimating the FRF under impact loads. The maximum posteriori estimation of the FRF is obtained, and the variance of the FRF estimation is also given. Furthermore, the numerical positive definiteness for optimizing the hyper-parameters is improved by applying QR decomposition. Finally, the effectiveness and reliability of the proposed method are verified by numerical examples and vibration experiments.