In this study, the proton dynamics of hydrogen bonds for two forms of crystalline aspirin was investigated by the Born-Oppenheimer molecular dynamics (BOMD) method. Analysis of the geometrical parameters of hydrogen bonds using BOMD reveals significant differences in hydrogen bonding between the two crystalline forms of aspirin, Form I and Form II. Analysis of the trajectory for Form I shows spontaneous proton transfer in cyclic dimers, which is absent in Form II. Quantization of the O-H stretching modes allows a detailed discussion on the strength of hydrogen-bonding interactions. The focal point of our study is examination of the hydrogen bond characteristics in the crystal structure and clarification of the influence of hydrogen bonding on the presence of the two crystalline forms of aspirin. In the BOMD method, thermal motions were taken into account. Solving the Schrodinger equation for the snapshots of 2D proton potentials, extracted from MD, gives the best agreement with IR spectra. The character of medium-strong hydrogen bonds in Form I of aspirin was compared with that of weaker hydrogen bonds in aspirin Form II. Two proton minima are present in the potential function for the hydrogen bonds in Form I. The band contours, calculated by using one- and two-dimensional O-H quantization, reflect the differences in the hydrogen bond strengths between the two crystalline forms of aspirin, as well as the strong hydrogen bonding in the cyclic dimers of Form I and the medium-strong hydrogen bonding in Form II.