In this work, we propose a reduced dimension and low complexity algorithm to estimate the direction-of-arrival (DOA), direction-of-departure (DOD) and the Doppler shift of a moving target for a multiple-input-multiple-output (MIMO) radar. We derive two cost functions based on two different objective functions. We solve each of the derived cost function with a low complexity fast-Fourier-transform (FFT)-based solution in three dimensions. We further carry out a derivation to reduce the three-dimensional search to two-dimensional (2D) search and solve it with a 2D-FFT. Another reduced dimension algorithm is derived using the generalized eigenvalue method which finds the estimate of unknown parameters in one dimension with less memory constraints. This way, we propose three algorithms based on the first cost function and another three algorithms based on the second. Simulation results are used to validate the proposed algorithms. We compare the mean-square-error (MSE) performance and computational complexity of our proposed algorithms with existing ones as well. We show that our proposed algorithms have better MSE performance than existing ones and achieves the Cramér-Rao lower bound (CRLB) for all unknown target parameters. The proposed algorithms exhibit lower computational complexity than the existing ones and also provide an estimate for the Doppler shift.