Nuclear　level　density　is　calculated　with　the　combinatorial　method　based　on　the　relativistic　density　functional　theory　including　pairing　correlations.　The　Strutinsky　method　is　adopted　to　smooth　the　total　state　density　in　order　to　refine　the　prediction　at　low　excitation　energy.　The　impacts　of　pairing　correlations　and　moments　of　inertia　on　the　nuclear　level　density　are　discussed　in　detail.　Taking　Cd-112　as　an　example,　it　is　demonstrated　that　the　nuclear　level　density　based　on　the　relativistic　density　functional　PC-PK1　can　reproduce　the　experimental　data　at　the　same　level　as　or　even　better　than　the　previous　approaches.