The magnetic torque of kappa-(BEDT-TFF)2CU(NCS)2 was measured as a function of field direction theta with respect to the a*-axis under constant magnetic fields, H, up to 8 kOe in the temperature range from 1.3 to 8 K. A sharp cusp, C1, in the irreversible region was found at theta(c1) near the H parallel-to bc-plane between 1.3 and 7 K. In addition, extra cusps, C2 and C3, Were observed at theta(c2) and theta(c3), respectively, between 2.5 and 6 K. At each temperature, the perpendicular component of H giving each cusp is kept constant as H cos theta(cn) = const = H(cPn) (n = 1, 2, 3), i.e., cusps C1, C2, and C3 are ruled by the characteristic field perpendicular to the bc-plane H(cP1), H(cP2), H(cP3), and H(cP3), respectively. These behaviors are almost the same as those we found in the oxide superconductor Bi2Sr2CaCu2O8. These results suggest that the cusps are intrinsic for irreversible vortex states of these layered superconductors.