In this paper, we propose DFT Beamspace Matrix pencil (BMP) method for direction of arrival estimation (DOA). The DFT beamspace approach has the advantage of reduced computational complexity due to converting complex computations (in Matrix Pencil method) into real ones along with the inherent ability to operate in a reduced beam-space in situations where some priori information is available about the DOAs. Furthermore, a novel Multiple Invariance BMP (MBMP) method is also developed and it is shown through simulations that its reduced beamspace version has comparable performance to the existing Unitary Matrix Pencil method (UMP) with lower computational cost.