The directions and gains of the paths with significant power can reconstruct mm-wave channel estimation, attributed to spatial sparsity resulting from severe propagation loss. Leveraging this feature, the two-dimensional beamspace method of direction estimation (2-D BMODE) is developed to estimate the path directions, including angles of departure and arrival. The least-squares(LS) method is then employed to estimate the path gains. Different from the beamspace two-dimensional multiple signal classification (MUSIC) method, the method proposed in this paper significantly ruduces computational complexity without spectral search. Moreover, the DODs and DOAs can be paired automatically by reduced-dimension(RD) MUSIC. Meanwhile, the performance of this method deteriorates when the covariance matrix of gains isn’t of full column rank. This paper also enhances the performance using spatial smoothing technique and oblique projecting to overcome the influence of rank deficiency. The 2-D BMODE method, as illustrated in this paper, outperforms in terms of both unity in computational complexity and estimation accuracy. Numerical simulations validate the advantages and demonstrate the method can serve as a superior alternative.