Relying　on　offloading　computation　tasks　to　the　network　edge,　ultra　dense　networks　(UDNs)　are　capable　of　providing　delay-aware　service　to　nearby　users.　Meanwhile,　software　defined　networking　(SDN)　is　deemed　as　an　effective　technology　to　ease　the　management　of　infrastructure　plane　and　control　plane　in　UDNs,　which　is　termed　as　SDN-based　ultra　dense　networks.　Specifically,　the　centralized　SDN　controller　is　capable　of　managing　the　whole　network　globally.　With　the　increasing　demands　for　various　applications　as　well　as　the　limitation　of　computation,　storage　and　communication　resource,　how　to　allocate　spectrum　resource　appropriately　is　imperative.　In　this　article,　we　mainly　show　solicitude　for　spectrum　sharing　and　edge　computation　offloading　problems　in　SDN-based　ultra　dense　networks,　constituted　of　various　macro　base　stations　(MBSs),　small-cell　base　stations　(SBSs)　and　user　equipments　(UEs).　To　address　this　issue,　we　propose　a　second-price　auction　scheme　for　ensuring　the　fair　bidding　for　spectrum　rent,　which　enables　the　MBS　edge　cloud　and　SBS　edge　cloud　to　occupy　the　channel　in　cooperative　and　competitive　modes.　Moreover,　the　MBS　edge　cloud　is　termed　as　the　buyer,　and　the　SBS　edge　clouds　are　the　sellers　who　sell　the　offloading　resource　to　the　MBS　edge　cloud.　To　be　specific,　the　spectrum　sharing　and　computation　offloading　scheme　is　executed　in　the　SDN　controller,　and　the　controller　is　responsible　for　distributing　spectrum　allocation　instructions　to　the　infrastructure　plane.　Finally,　experimental　results　validate　the　effectiveness　of　our　proposed　scheme　in　SDN-based　ultra　dense　networks.