We prove that subparacompact mappings inversely preserve 2-subparacompactness. As some applications of the above result, we obtain that both perfect mappings and closed Lindelof regular mappings inversely preserve 2-subparacompactness, which answer a question on 2-subparacompactness posed by Qu and Yasui affirmatively. Also we give a counterexample to show that closed Lindelof mappings do not inversely preserve 2-subparacompactness.