An efficient joint transmit and receive antenna selection method is proposed for rank-deficient MIMO channels. The capacity performance of the rank-deficient channel matrix is analyzed and the conclusion is reached that a judicious selection of transmit antennas can even increase the system capacity. To retrieve the full-rank channel matrix from the original rank-deficient channel matrix and to maintain the channel capacity as much as possible, the transmit antenna selection is then completed first. The orthogonal subspace projection of the original rank-deficient channel matrix is exploited to reduce the computational complexity of the transmit antenna selection. For the receive antenna selection, the recently proposed maximal-volume-based fast receive antenna selection algorithm is used and extended to achieve a joint transmit and receive antenna selection， in which the maximum-volume sub-matrix of the original channel matrix is directly and rapidly searched. Due to its global-search capability, a better capacity performance is realized under the condition of moderate to high SNRs than using the existing 'local-search' and greedy antenna selection methods and almost the same capacity performance as the optimal selection method based on a 2D exhaustive search is attained. Furthermore, due to the use of the rank-one updating procedure combined with a reduced number of iteration steps, the computational load of our joint transmit and receive antenna selection method fits for real-time applications. Numerical results are presented to verify the validity of the proposed method.