The principle of the inverse cherenkov focusing laser accelerator is presented. It is readily shown, by studying the dynamics of the charged particles, that the particles are accelerated steadily and continuously when the condition of the cherenkov radiation is satisfied, and need no additional focusing systems since the laser field on the focusing axis is just the accelerating field, so that the intensity of the latter may be higher than that in the previously proposed inverse cherenkov laser accelerator. The limitations of this accelerating mechanism are also discussed.