Optical properties, such as the attenuation coefficients of multi-layer tissue samples, could be used as a biomarker for diagnosis and disease progression in clinical practice. In this paper, we present a method to estimate the attenuation coefficients in a multi-layer sample by fitting a single scattering model for the OCT signal to the recorded OCT signal. In addition, we employ numerical simulations to obtain the theoretically achievable precision and accuracy of the estimated parameters under various experimental conditions. Finally, the method is applied to two sets of measurements obtained from a multi-layer phantom by two experimental OCT systems: One with a large and one with a small Rayleigh length. Numerical and experimental results show an accurate estimation of the attenuation coefficients when using multiple B-scans.