Abstract.Anisotropic lattice QCD studies of penta-quarks(5Q) with J P = 1/2 ± and 3/2 ± are presented at the quenched level together with tetra-quarks(4Q). The standard gauge action at β = 5.75 and O(a) improved quark (clover) action with κ = 0.1410(0.010)0.1440 are employed on the anisotropic lattice with the renormalized anisotropy a s /a t = 4. The "hybrid boundary condition(HBC)" is adopted to discriminate a compact resonance state from scattering states. Only massive 5Q states are found for J P = 1/2 + and 3/2 ± , which cannot be identified as Θ + (1540). A low-lying 5Q state is found for J P = 1/2 − at m 5Q ≃ 1.75 GeV, which however turns out to be an NK scattering state through the HBC analysis. A preliminary result for 4Q states is presented suggesting an existence of a compact 4Q resonance at m 4Q ≃ 1.1 GeV in the idealized SU(4) f chiral limit.Keywords: Exotic hadron, lattice QCD PACS: 12.38. Gc, 12.39.Mk, 14.20.Jn Multi-quark states attract an increasing interest from wide range of high energy physics. Enormous number of experimental as well as theoretical contributions have been devoted to the penta-quarks(5Q) [1,2,3,4,5,6], and series of tetra-quark(4Q) candidates have been discovered recently as D + s0 (2317) [7,8] and Y (4260). In this paper, we are interested in 5Q Θ + (1540) and 4Q D + s0 (2317). We adopt 12 3 × 96 anisotropic lattice QCD for high precision measurements, where the temporal lattice spacing is 4 times finer than the spatial ones as a s /a t = 4. We employ standard gauge action at β = 5.75 and O(a) improved Wilson (Clover) action with κ = 0.1410(0.010)0.1440, which roughly covers the quark mass region of m s ≤ m q ≤ 2m s . κ s = 0.1440 is fixed for s quark, and the chiral extrapolation is performed by varying κ = 0.1410 − 0.1440 for u and d quarks. The lattice spacing is determined with the Sommer parameter r −1 0 = 395 MeV leading to the spatial lattice spacing as a −1 s = 1.10 GeV (a s ≃ 0.18 fm). We use 504 gauge configurations for J P = 1/2 ± penta-quarks, 1000 gauge configurations for J P = 3/2 ± penta-quarks, and 1872 gauge configurations for tetra-quarks. A smeared source with gaussian size ρ ≃ 0.4 fm is adopted after Coulomb gauge fixing to suppress the contamination of excited states.We use the hybrid boundary condition(HBC) [4] as well as the conventional periodic BC(PBC) to discriminate a compact resonance state from two-hadron scattering states. HBC is a flavor-dependent spatial BC, where we impose PBC on s quark, and anti-PBC on u and d quarks. Since Θ + (uudds) contains even number of u and d quarks, it obeys