The　terahertz　nonlinear　optical　response　in　Kronig-Penney　(KP)　type　graphene　superlattice　is　demonstrated.　The　single-,　triple-　and　quintuple-frequencies　of　the　fifth-order　nonlinear　responses　are　investigated　for　different　frequencies　and　temperatures　with　the　angle　phi　along　the　periodicity　of　the　superlattice　toward　the　external　field　tuning　from　0　to　pi/2.　The　results　show　that　the　fifth-order　nonlinear　optical　conductance　of　graphene　superlattice　is　enhanced　in　the　terahertz　regime　when　phi　=　0,　i.e.　an　external　field　is　applied　along　the　periodicity　of　the　superlattice.　The　fifth-order　nonlinear　optical　conductances　at　phi　=　0　for　different　frequencies　and　temperatures　are　calculated.　The　results　show　that　the　nonlinear　optical　conductance　is　enhanced　in　low　frequency　and　low　temperature.　Our　results　suggest　that　KP　type　graphene　superlattices　are　preferred　structures　for　developing　graphene-based　nonlinear　photonics　and　optoelectronics　devices.