Modern cephalopods are notably the most intelligent invertebrates and this is accompanied by keen vision. Despite extensive studies investigating the visual systems of cephalopods, little is known about their visual perception and object recognition. In the present study, we investigated the visual processing of the cuttlefish Sepia pharaonis, including visual equivalence and amodal completion. Cuttlefish were trained to discriminate images of shrimp and fish using the operant conditioning paradigm. After cuttlefish reached the learning criteria, a series of discrimination tasks were conducted. In the visual equivalence experiment, several transformed versions of the training images, such as images reduced in size, images reduced in contrast, sketches of the images, the contours of the images, and silhouettes of the images, were used. In the amodal completion experiment, partially occluded views of the original images were used. The results showed that cuttlefish were able to treat the training images of reduced size and sketches as the visual equivalence. Cuttlefish were also capable of recognizing partially occluded versions of the training image. Furthermore, individual differences in performance suggest that some cuttlefish may be able to recognize objects when visual information was partly removed. These findings support the hypothesis that the visual perception of cuttlefish involves both visual equivalence and amodal completion. The results from this research also provide insights into the visual processing mechanisms used by cephalopods.