A hologram display apparatus and a hologram display method are provided. The hologram display apparatus includes a controller and a display device. The controller is configured to obtain plural grayscale values Gi of an image of a to-be-displayed object, generate plural display sub-image codes Qj according to the plurality of grayscale values Gi and transmit the plurality of display sub-image codes Qj to the display device, where i=1, 2, . . . , m, j=1, 2, . . . N, each of m and N is a positive integer. The display device is configured to generate and display plural sub-holograms according to the plurality of display sub-image codes, a quantity of the plurality of sub-holograms being equal to that of the plurality of display sub-image codes, such that the plurality of sub-holograms are superimposed to generate a hologram of the image of the to-be-displayed object in human eyes.