Orbital angular momentum (OAM) multiplexing suffers from inter-mode interference (IMI) due to a beam axis misalignment. However, the traditional IMI cancellation method assumes that the IMI rises from all OAM modes, which results in heavy computational loads. This paper proposes an efficient IMI cancellation method for OAM multiplexing in the presence of a beam axis misalignment. In the proposed method, considering that the interference from adjacent OAM modes is dominant in such a misalignment, IMI cancellation is performed by considering only the neighboring OAM modes. This method can reduce the computational cost while retaining the transmission performance. Moreover, the minimum mean square error (MMSE) is adopted as the equalizer criterion to suppress noise enhancement. The effectiveness of the proposed method as compared with the traditional IMI cancellation method is demonstrated in terms of the system capacity and computational complexity through computer simulations.