Neutron star (NS) is an ideal place to capture the interstellar dark matter (DM) due to its strong gravity and high baryonic density. We study the effects of self-interacting DM which is captured by NS and thermalized with the core. By adjusting the parameters of DM such as mass, number density, DM-nucleon cross-section and DM-DM cross-section, we investigate the possibility of the captured DM particles to reach the collapse condition of black hole (BH) in NS core. In particular, for the case of DM is a bosonic particle, the Bose-Einstein Condensate (BEC) might play a role during accumulation. We simulate the cooling processes of NS and the thermalization condition with DM. We discuss the number evolution of DM according to the interplay between thermalization and BEC.