In the second-harmonic generation processes involving Laguerre-Gaussian (LG) beams, the generated second-harmonic wave is generally composed of multiple modes with different radial quantum numbers. To generate single-mode second-harmonic LG beams, a type of improved quasi-phase-matching method is proposed. The Gouy phase shift has been considered in the optical superlattice designing and an adjustment phase item is introduced. By changing the structure parameters, each target mode can be phase-matched selectively, whose purity can reach up to 95%. The single LG mode generated from the optical superlattice can be modulated separately and used as the input signals in the mode division multiplexing system.