This　study　presents　a　new　framework　to　solve　the　coupled　semilinear　elliptic　equation　by　the　domain　decomposition　algorithm.　Unlike　the　traditional　domain　decomposition　algorithm,　the　coupled　semilinear　elliptic　equation　doesn＇t　need　to　be　solved　directly.　The　strategy　is　to　construct　a　set　of　nested　finite　element　spaces,　and　subsequently　solve　some　decoupled　linear　elliptic　equations　by　using　the　domain　decomposition　method　in　each　level　space.　Additionally,　a　small-scale　coupled　semilinear　elliptic　equation　in　a　specially　designed　correction　space　will　be　solved.　As　the　large-scale　coupled　semilinear　elliptic　equation　doesn＇t　need　to　be　solved　directly,　there　will　be　an　improved　efficiency　as　compared　to　the　traditional　domain　decomposition　method.　Furthermore,　as　the　domain　decomposition　method　is　only　used　to　solve　decoupled　linear　elliptic　equations,　any　efficient　algorithms　designed　for　the　associated　linear　elliptic　equations　can　be　incorporated　in　the　proposed　algorithm　framework.　Thus,　the　algorithm　is　highly　flexible.　Additionally,　it　can　be　theoretically　proven　that　the　proposed　algorithm　has　very　low　requirements　for　the　smoothness　of　nonlinear　terms.