The quasi-potential approach is used to project a four-dimensional field-theoretical model of a three-particle system to the light-front (LF) valence sect or. The starting point is the Bethe-Salpeter equation (BSE) for three particles in the ladder approximation. The projection technique allows to eliminate three-body reducible diagrams from the kernel of the LF integral equation for the valence wave function. We construct the next-to-leading order contribution to the kernel of the LF three-body integral equation. We exemplify the method for a three-boson system with a contact interaction.