We have applied a method of absorbing boundary condition (ABC) to calculations of the level density (LD) and the continuum level density (CLD). The results of LD and CLD in the ABC calculation are compared with those calculated by complex scaling method (CSM). The energy dependence of LD in ABC shows the similar behavior to those in CSM around the resonance energy but they are prominently different especially at the lower energy region due to the different sequence of the energy eigenvalues in the complex plane. The phase shift for two-body scattering problems is also derived from CLD. The phase shift obtained by ABC is almost the same as that calculated from CSM although the ABC method seems to be a little inferior to the CSM calculation in the numerical precision. The improvement of the numerical precision in ABC is also discussed.