A Cherenkov imaging camera for the CANGAROO-III experiment has been developed for observations of gamma-ray-induced air showers at energies from 10(11) to 10(14) eV. The camera consists of 427 pixels, arranged in a hexagonal shape at 0.17degrees intervals, each of which is a 3/4in. diameter photomultiplier module with a Winston-cone-shaped light guide. The camera was designed to have a large dynamic range of signal linearity, a wider field of view, and an improvement in photon-collection efficiency compared with the CANGAROO-II camera. The camera, and a number of the calibration experiments made to test its performance, are described in detail in this paper. (C) 2003 Elsevier Science B.V. All rights reserved.