We investigate various properties of ${kappa}$-net convergence structures and define a ${kappa}$-net-based continuous function on ${kappa}$-net $mathcal{L}^+$-convergence structures, and study relationships between continuity and ${kappa}$-net-based continuity on ${kappa}$-net $mathcal{L}^+$-convergence structures. We also provide some characterizations of ${kappa}$-net-based continuity.