The　authors　construct　an　IPO　selling　mechanism　with　risk　neutral　retail　investors,　and　two　institutional　investors　that　are　better-informed　and　less-informed,　respectively.　In　the　mechanism,　in　addition　to　the　main　constraints　such　as　the　individual　rationality　(IR),　the　incentive　compatibility　(IC),　and　the　feasibility　constraint　(FC),　the　authors　consider　two　more　typical　constraints:　There　is　a　lower　bound　and　no　bound　for　allocation　of　the　shares　to　two　institutional　investors.　The　authors　derive　the　explicit　expression　of　the　optimal　allocation　of　the　shares　to　the　investors.　Under　the　lower　bound　constraint,　the　optimal　mechanism　will　encourage　the　better-informed　bidder　to　report　sufficiently　higher　signal　in　order　to　get　shares.　If　he　gets　allocation　of　shares,　then　the　higher　signal　he　reports,　the　more　shares　he　will　get,　and　the　more　the　issuer’s　expected　maximum　revenue　will　be.　©　2016,　Institute　of　Systems　Science,　Academy　of　Mathematics　and　Systems　Science,　CAS　and　Springer-Verlag　Berlin　Heidelberg.