Quantum transport of holes in one-, two- and three-dimensional devices is simulated based on the 6-band k . p method. Detailed numerical aspects for an efficient development of a k . p-based simulator are provided. In particular, real-space and k-space discretization schemes for devices of different dimensionality are described and their effectiveness in numerical implementation is compared. The mode-space approach for drastic reduction of computation time is also described. The capability of the k . p-based simulator is demonstrated by investigating various aspects of hole transport in devices of different dimensionality.