Sperm whales are present in the Canary Islands year-round, suggesting that the archipelago is an important area for this species in the North Atlantic. However, the area experiences one of the highest reported rates of sperm whale ship-strike in the world. Here we investigate if the number of sperm whales found in the archipelago can sustain the current rate of ship-strike mortality. The results of this study may also have implications for offshore areas where concentrations of sperm whales may coincide with high densities of ship traffic, but where ship-strikes may be undocumented. The absolute abundance of sperm whales in an area of 52933 km2, covering the territorial waters of the Canary Islands, was estimated from 2668 km of acoustic line-transect survey using Distance sampling analysis. Data on sperm whale diving and acoustic behaviour, obtained from bio-logging, were used to calculate g(0) = 0.92, this is less than one because of occasional extended periods when whales do not echolocate. This resulted in an absolute abundance estimate of 224 sperm whales (95% log-normal CI 120–418) within the survey area. The recruitment capability of this number of whales, some 2.5 whales per year, is likely to be exceeded by the current ship-strike mortality rate. Furthermore, we found areas of higher whale density within the archipelago, many coincident with those previously described, suggesting that these are important habitats for females and immature animals inhabiting the archipelago. Some of these areas are crossed by active shipping lanes increasing the risk of ship-strikes. Given the philopatry in female sperm whales, replacement of impacted whales might be limited. Therefore, the application of mitigation measures to reduce the ship-strike mortality rate seems essential for the conservation of sperm whales in the Canary Islands.