In this paper, a biquaternion beamspace, constructed by projecting the original data of an electromagnetic vector-sensor array into a subspace of a lower dimension via a quaternion transformation matrix, is first proposed. ; To estimate the direction and polarization angles of sources, biquaternion beamspace multiple signal classification (BB-MUSIC) estimators are then formulated. The analytical results show that the biquaternion beamspaces offer us some additional degrees of freedom to simultaneously achieve three goals. One is to save the memory spaces for storing the data covariance matrix and reduce the computation efforts of the eigen-decomposition. Another is to decouple the estimations of the sources’ polarization parameters from those of their direction angles. The other is to blindly whiten the coherent noise of the six constituent antennas in each vector-sensor. It is also shown that the existing biquaternion multiple signal classification (BQ-MUSIC) estimator is a specific case of our BB-MUSIC ones. ; The simulation results verify the correctness and effectiveness of the analytical ones.