We investigate the current-induced spin polarization in the two-dimensional hole gas (2DHG) with the structure inversion asymmetry. By using the perturbation theory, we re-derive the effective $k$-cubic Rashba Hamiltonian for 2DHG and the generalized spin operators accordingly. Then based on the linear response theory we calculate the current-induced spin polarization both analytically and numerically with the disorder effect considered. We have found that, quite different from the two-dimensional electron gas, the spin polarization in 2DHG depends linearly on Fermi energy in the low doping regime, and with increasing Fermi energy, the spin polarization may be suppressed and even changes its sign. We predict a pronounced peak of the spin polarization in 2DHG once the Fermi level is somewhere between minimum points of two spin-split branches of the lowest light-hole subband. We discuss the possibility of measurements in experiments as regards the temperature and the width of quantum wells.
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