This paper presents a new adaptive torque estimation algorithm for an interior permanent magnet synchronous motor (IPMSM) with parameter variations and cross-coupling between d- and q-axis dynamics. All cross-coupled, time-varying, or uncertain terms that are not part of the nominal flux equations are included in two equivalent mutual inductances, which are described using the equivalent d- and q-axis back electromotive forces (EMFs). The proposed algorithm estimates the equivalent d- and q-axis back EMFs in a recursive and stability-guaranteed manner, in order to compute the equivalent mutual inductances between the d- and q-axes. Then, it provides a more accurate and adaptive torque equation by adding the correction terms obtained from the computed equivalent mutual inductances. Simulations and experiments demonstrate that torque estimation errors are remarkably reduced by capturing and compensating for the inherent cross-coupling effects and parameter variations adaptively, using the proposed algorithm.