The presented work considers a two-point boundary value problem for a system of differential equations subject to impulse action at a non-fixed moment in time. The problem under consideration is studied based on the ideas of the parameterization method. One of the ways to find an approximate solution to the problem under consideration is proposed. A test example is given that shows the effectiveness of the proposed method for finding an approximate solution to a two-point boundary value problem for a system of differential equations subject to impulse action at a non-fixed point in time.