Neutron stars can accrete dark matter particles by the interaction between baryonic matter and dark matter. Under certain conditions, dark matter particles accreted by a neutron star can induce gravitational collapse and then form a small black hole, which may grow and consume the neutron star. In this paper, based on the present model, we obtain constraints on the dark matter particle -- neutron cross-section at different dark matter particle masses. We adopt the Weakly Interacting Massive Particle (WIMP) model and consider that dark matter particles are bosons. We get how self-interaction and annihilation of dark matter particles impact the constraints on dark matter.We consider two existing neutron stars to bound the parameter space of dark matter. In addition,we consider two hypothetical neutron stars, which could be detected in the future. We predict possible constraints on the parameter space of dark matter.For bosonic dark matter particles which can form Bose-Einstein Condensate (BEC), assuming that there is no or only weak self-interaction and weak annihilation,we find that constraints from neutron stars are stronger than their direct detection experiments including XENON1T.Future detection of old neutron stars near the Galactic center may improve the bounds of parameter of dark matter particles in this model, thus can advance our knowledge of dark matter.