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Multiple-input multiple-output (MIMO) radar has received much attention due to its potentials in offering improved performance for target detection and parameter estimation. It has been shown that the performance of direction finding techniques can be considerably enhanced in MIMO radar, since an extended virtual array can be employed. In general, the performance gain is achieved by assuming that both the transmitter and receiver are well calibrated without uncertainties. However, in practice, both the transmitter and receiver may suffer from various array imperfections such as mutual coupling. Hence, the problem of direction finding in MIMO radar with unknown mutual coupling is investigated in this paper. Computationally efficient algorithms are developed to estimate the directions-of-arrival by exploiting the structure of mutual coupling matrix of the transmitter and receiver equipped with uniform linear arrays. Moreover, it is shown that the proposed methods can be applied to scenarios in which the transmitter or receiver has other imperfections, for example, sensor position perturbations or gain/phase mismatches. Simulation results demonstrate that the proposed methods are able to effectively eliminate the negative influence of unknown mutual coupling on direction finding and offer improved performance over the existing methods.