A　vertical-cavity　surface-emitting　laser　(VCSEL)　is　easily　made　into　a　two-dimensional　array　to　improve　its　output　power.　However,　if　the　near-field　complex　amplitude　output　cannot　be　stabilized　in　the　lowest　supermode　generated　by　the　fundamental　transverse　mode,　the　spot　cannot　converge　on　the　center　normal　of　the　far-field　array　geometry,　and　the　energy　will　be　diverged.　The　external　cavity　is　prepared　for　the　VCSEL　array,　and　the　output　of　the　array　can　be　stabilized　in　the　lowest　order　supermode　generated　by　the　fundamental　transverse　mode　by　supermode　control　through　diffraction　coupling.　In　this　study,　the　parallel-coupled　model　for　the　2-dimensional　VCSEL　array　based　on　Fresnel　diffraction　integration　was　established　and　used　to　numerically　calculate　and　analyze　the　influence　on　the　supermodes＇　thresholds　of　different　array　distributions,　array　elements＇　transverse　modes　and　duty　ratios　versus　the　length　of　the　external　cavity.　The　simulation　results　show　that　the　square　array　provides　a　wider　range　of　external　cavity　control　length　(0.2d(2)/lambda　and　approximately　0.9　to　1.0d(2)/lambda).　The　lowest　supermode　of　the　fundamental　transverse　mode　can　be　outputted.　For　the　regular　hexagonal　array　with　the　length　of　the　external　cavity　of　0.15d(2)/lambda　and　0.6d(2)/lambda.　The　results　have　important　reference　significance　for　the　design　of　an　external　cavity　VCSEL　array,　which　can　control　the　supermode　and　obtain　VCSEL　coherent　array　beams　with　high　power　and　near　diffraction　limits.