Ride-hailing services are growing rapidly and becoming one of the most disruptive technologies in the transportation realm. Accurate prediction of ride-hailing trip demand not only enables cities to better understand people's activity patterns, but also helps ride-hailing companies and drivers make informed decisions to reduce deadheading vehicle miles traveled, traffic congestion, and energy consumption. In this study, a convolutional neural network (CNN)-based deep learning model is proposed for multi-step ride-hailing demand prediction using the trip request data in Chengdu, China, offered by DiDi Chuxing. The CNN model is capable of accurately predicting the ride-hailing pick-up demand at each 1-km by 1-km zone in the city of Chengdu for every 10 minutes. Compared with another deep learning model based on long short-term memory, the CNN model is 30% faster for the training and predicting process. The proposed model can also be easily extended to make multi-step predictions, which would benefit the on-demand shared autonomous vehicles applications and fleet operators in terms of supply-demand rebalancing. The prediction error attenuation analysis shows that the accuracy stays acceptable as the model predicts more steps.