In this paper, monostatic MIMO radar with cross array using electromagnetic vector antennas is utilized and a novel algorithm for fast Two Dimensional (2D) Direction Of Arrival (DOA) with high accuracy and polarization estimation is proposed. First, given the virtual steering vector of monostatic MIMO radar, a reduced-dimensional matrix is employed and the high dimensional received data is transformed into a lower dimensional signal space via the reduced-dimensional transformation. Then the Propagator Method (PM) is utilized to estimate the corresponding signal subspace by linear operation. Second, rotational invariance relationships with long baseline in the proposed scheme and polarization vector cross product between the normalized electric vector and the normalized magnetic vector can be used to obtain the 2D DOA estimation with high accuracy and non-ambiguity. The polarization rotational invariance relationship, which is irrespective of array geometry, is utilized to estimate the auxiliary polarization angle and polarization phase difference. The proposed system, extending array aperture without increasing sensors and hardware costs, can obtain the waveform diversity offered by MIMO radar and the polarization diversity offered by vector sensor together and achieve better estimation performance. Meanwhile, through the reduced-dimensional and linear operation, the proposed algorithm, obtaining signal to ratio gain and joint estimation for 2D DOA with high accuracy and 2D polarization parameters with automatic pairing, can reduce the dimension of received data and the computational complexity of parameters estimation effectively. Lastly, simulation results verify the correctness of theoretical analysis and the effectiveness of proposed algorithm.