Abstract: To study the growth patterns of (BN)_n(n=1～20) clusters, the geometrical and electronic structure of (BN)_n(n=1～20) clusters are optimized by using density functional theory(B3LPY) at the 6-31g(d) level. The basic parameters of the ground-state stable structure of (BN)_n(n=1～20) clusters, including symmetry, HOMO, LUMO and energy gap, are obtained by analyzing the harmonic frequencies and calculating the binding energy. On the basis of the above studies, the first-order (ΔE_n) and second-order (Δ²E_n) differences of total energies are further analyzed, and it is found that the B₁₆N₁₆ clusters with T_D point group is the most stable in many (BN)_n(n=1～20) clusters. The cluster stability is good when n=3, 5, 8, 10, 14, 16, 18, and relatively poor when n=2, 4, 6, 9, 12, 15, 17, 19. The IR-Raman spectrums of (BN)_n(n=1～20) clusters increase with the increasing of n values. Based on their geometric structures, the absorption spectrums are calculated using time-dependent density functional theory (TD-DFT) with the same basis set and employing the polarizable continuum medium model(PCM). The results show that the UV-Vis absorption intensities and ε(L/mol/cm) values of (BN)_n(n=1～20) clusters increase with the increasing of n value, and the peaks of absorption waves also increasing.