Introduction: Since 2015, the research group Biophysics & Structural Biochemistry at the Pontificia Universidad Javeriana (PUJ), in cooperation with the International Atomic Energy Agency (IAEA), has been working on Neutron Capture Therapy (NCT), together with graduate students of the Master Program in Medical Physics at PUJ. Within our research program, one of the main goals is to learn and implement new numerical methods to study the neutron transport problem using the Boltzmann transport equation. In this paper we use the lattice Boltzmann method (LBM) to solve the time-dependent one-dimensional transport equation for monoenergetic neutral particles in a homogenous semi-infinite medium with isotropic scattering. Methods and Materials: The LBM for transient neutron transport problem is adapted from the phase space discretization of the standard neutron transport equation where the collision and streaming processes at each time step are specified through the calculation of the relaxation time and equilibrium particle distribution function suggested by the Bhatnagar-Gross-Krook (BGK) approximation. In order to apply the one-dimensional neutron transport lattice Boltzmann-BGK model for a homogeneous half-space with isotropic scattering problem, a computational algorithm in Matlab has been made. The time-dependent neutron flux and deposited dose for different macroscopic cross section values have been obtained. Results: Simulation results show that the LBM can be effectively applied to study the 1-D neutron transport process with a reduced computational cost leading to a consistent description of neutral particles interaction with matter. Conclusions: We have shown that the proposed approach provides a powerful alternative for solving the Boltzmann transport equation required to characterize neutron distributions and other ionizing radiations for a given geometry. This methodology can be also considered as an alternative numerical technique for the treatment of particle transport problem.