Most existing amplitude variation with angle (AVA) inversions are based on the exact Zoeppritz equation or its approximations. These modeling methods, which are ray-tracing-based and describe P-wave primary reflections only, lead to exacting requirements for pre-processing of the input data. Current processing is inadequate to satisfy these demands, especially for removing the effects of transmission losses, P-wave multiples and various converted-wave modes. By using input data with processing errors, inversion results of primary-only methods are predictably not accurate enough. The propagator matrix (PM), like the reflectivity method, uses an analytical solution to the wave equation and considers full-wave propagation effects in horizontal or nearly horizontal multilayered earth models. The numerical examples verify that a PM can effectively estimate transmission losses, multi-reflections and the comprehensive responses of thin interbedded layers, and also has higher reflection sensitivities to P-wave and S-wave velocity and density, as compared with ray-tracing-based AVA modelling. A pre-stack AVA three-parameter inversion by using a PM as the forward engine is proposed. Following a Bayesian approach, the inversion is stabilized by including the correlation of P-wave velocity, S-wave velocity and density. For inversion accuracy, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) optimization method is used to solve the augmented function, and the generalized cross-validation (GCV) criterion (Huang et al. in J Geophys Eng 14(1):100–112, 2017) is introduced to adaptively acquire the regularization parameter. Theoretical model inversion analysis shows that the proposed inversion can make use of transmission losses, P-wave multiples and converted wave modes, which not only cost-effectively simplifies the pre-processing, but also generates reasonable inverted results for multilayered conditions. The proposed inversion is then applied to a set of real data, and a comparison with Zoeppritz equation-based inversion demonstrates that PM inversion is clearly superior to Zoeppritz equation-based inversion in terms of stability and accuracy.