Anthropogenic carbon dioxide (CO2) emissions are being absorbed by the oceans, a process known as ocean acidification, and risks adversely affecting a variety of behaviours in a range of marine species, including inhibited learning in some fishes. However, the effects of elevated CO2 on learning in advanced invertebrates such as cephalopods are unknown. Any impacts to the learning abilities of cephalopods could have far-reaching consequences for their populations and the communities they inhabit. Cephalopods have some of the most advanced cognitive abilities among invertebrates and are one of the few invertebrate taxa in which conditional discrimination has been demonstrated, though the trait has not been demonstrated in any species of squid. Here, we tested for the first time the capacity for conditional discrimination in a squid species (Sepioteuthis lessoniana). Furthermore, we investigated the effects of projected future CO2 levels (1,084 µatm) on conditional discrimination and learning more generally. A three-task experiment within a two-choice arena was used to test learning and conditional discrimination. Learning was measured by improvements in task completion in repeated trials over time and the number of trials required to pass each task. Squid exhibited significant learning capabilities, with an increase in correct choices over successive trials and a decrease in the number of trials needed to complete the successive tasks. Six of the 12 squid tested successfully passed all three tasks indicating a capacity for conditional discrimination in the species. Elevated CO2 had no effect on learning or on the capacity for conditional discrimination in squid. This study highlights the remarkable cognitive abilities of S. lessoniana, demonstrated by their capacity for conditional discrimination, and suggests that ocean acidification will not compromise learning abilities. However, other behavioural traits in the species have been shown to be altered at comparable elevated CO2 conditions. It is not clear why some ecologically important behaviours are altered by elevated CO2 whereas others are unaffected. Future research should focus on the physiological mechanism responsible for altered behaviours in squid at elevated CO2.