In this work, we introduce a Dynamically Sparse Discrete Velocity Method (DSDVM) for solving the Boltzmann-BGK equation. The distribution function is decomposed into two parts: an equilibrium component represented by the Maxwellian distribution and a non-equilibrium component. Discrete velocity points are allocated only to the non-equilibrium part, resulting in a significantly reduced number of velocity points, particularly in near-continuous regimes, which greatly lowers the computational cost compared to conventional discrete velocity methods. The discretization of the microscopic velocity space is dynamically and adaptively adjusted based on the non-equilibrium component of the distribution. Several numerical examples are presented to validate the efficiency and accuracy of the proposed DSDVM.