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A non-Abelian geometric method is proposed for rotating of heavy hole spinsin a singly positive charged quantum dot in Voigt geometry. The key ingredientis the delay-dependent non-Abelian geometric phase, which is produced by thenonadiabatic transition between the two degenerate dark states. We demonstrate,by controlling the pump, the Stokes and the driving fields, that the rotationsabout $y$- and $z$-axes with arbitrary angles can be realized with highfidelity. Fast initialization and heavy hole spin state readout are alsopossible.

Optical rotation of heavy hole spins by non-Abelian geometrical means