A theoretical study of geometrical structures and electronic properties of Be atom doped boron clusters BeB _n^0/- (n = 10–15) is performed using the CALYPSO approach for the global minimum search followed by density functional theory calculations. It is found that the global minima obtained for the BeB _10^0/- , BeB _11^- , BeB _12^0/- , and BeB _14^- clusters correspond to the quasi-planar or planar structures. However, the global minima obtained for the BeB₁₁, BeB₁₃, BeB _13^- , BeB₁₄ clusters correspond to the half-sandwich, cone, cage, squashed tubular structures, respectively. Interestingly, both the neutral and anionic BeB _15^0/- clusters have the axially chiral isomers which are chiral with degenerate enantiomers. Natural population analyses reveal that partial charge on Be atom transfer to boron atoms. The average binding energy values of BeB _n^0/- (n = 10–15) indicate that anionic clusters are overall more stable than the corresponding neutral ones, and both neutral and anionic clusters show the same trend that the stability increases gradually with the increase of B atoms number n. Chemical bonding analyses of closed-shell BeB₁₀, BeB _11^- , BeB₁₂ clusters reveal that the σ bonds stabilize whole molecular skeleton, and delocalized π bonds render the structure more stable. Furthermore, the three quasi-planar closed-shell clusters possess 3 delocalized π bonds, which quite surprisingly follow the 4m + 2 Hückel rule for aromaticity. Average polarizability of single atom for each quasi-planar or planar structure is larger than other structures, it indicates that quasi-planar or planar structure has stronger electron delocalization. Specifically, BeB _13^- and BeB _14^- with large first static hyperpolarizability can lead to the remarkable NLO response. The calculated spectra indicate that BeB _n^0/- (n = 10–15) have the meaningful characteristic peaks which can be compared with future experimental values. Our work enriches the database of geometrical structures of doped boron clusters and can provide much insight into the new doped boron clusters.