The angular misalignment of the tapered roller contact pair aggravates the stress edge effect and the stress concentration effect at the contact field, which in turn would affect bearing capacity and fatigue life of the contact pair. In this paper, based on the angular misalignment, the geometric interference model of the tapered roller contact pair was established. And two types of logarithmic crowning models for the roller profile design were theoretically deduced, in which design redundancy was considered through the quadratic processing of the pre-pressure. Then, with the discrete convolution and fast Fourier transform (DC-FFT) method and the conjugate gradient method (CGM), contact characteristics of the tapered roller with these two logarithmic profiles were verified. The results show that two profiles can effectively prevent the stress edge/concentration effect, improve contact pressure distribution and stress field of the roller in misalignment state, and ensure that the contact condition in alignment state is not greatly affected. The logarithmic crowning scheme is also suitable for the profile design of heavy-duty tapered rollers and can provide a reference for the crowning of other finite-line contact pairs under angular misalignment.