The current from a p-type quantum well caused by the hole tunneling in applied electric field, is calculated theoretically for semiconductors with the valence band described by the Luttinger's Hamiltonian. Although the ground state in a well is formed by heavy holes, at nonzero hole momenta, it contains the admixture of light hole states with a low effective mass and high probability of tunneling through the barrier. This fact increases the dark current by several orders of magnitude, as compared with a primitive theory assuming light and heavy holes as independent particles. The current-voltage characteristic for a dark current is calculated and its dependences on quantum well parameters and doping level are discussed. (C) 1998 American Institute of Physics.