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Hole spin relaxation in $p$-type (111) GaAs quantum wells is investigated inthe case with only the lowest hole subband, which is heavy-hole like in (111)GaAs/AlAs and light-hole like in (111) GaAs/InP quantum wells, being relevant.The subband L\"{o}wdin perturbation method is applied to obtain the effectiveHamiltonian including the Dresselhaus and Rashba spin-orbit couplings. Under aproper gate voltage, the total in-plane effective magnetic field in (111)GaAs/AlAs quantum wells can be strongly suppressed in the whole momentum space,while the one in (111) GaAs/InP quantum wells can be suppressed only on aspecial momentum circle. The hole spin relaxation due to the D'yakonov-Perel'and Elliott-Yafet mechanisms is calculated by means of the fully microscopickinetic spin Bloch equation approach with all the relevant scatteringsexplicitly included. For (111) GaAs/AlAs quantum wells, extremely longheavy-hole spin relaxation time (upto hundreds of nanoseconds) is predicted. Inaddition, we predict a pronounced peak in the gate-voltage dependence of theheavy-hole spin relaxation time due to the D'yakonov-Perel' mechanism. Thispeak origins from the suppression of the unique inhomogeneous broadening in(111) GaAs/AlAs quantum wells. Moreover, the Elliott-Yafet mechanism influencesthe spin relaxation only around the peak area due to the small spin mixingbetween the heavy and light holes in quantum wells with small well width. Wealso show the anisotropy of the spin relaxation. In (111) GaAs/InP quantumwells, a mild peak, similar to the case for electrons in (111) GaAs quantumwells, is also predicted in the gate-voltage dependence of the light-hole spinrelaxation time. The contribution of the Elliott-Yafet mechanism is alwaysnegligible in this case.