Recently, wireless caching techniques have been studied to satisfy lower delay requirements and offload traffic from peak periods. By storing parts of the popular files at the mobile users, users can locate some of their requested files in their own caches or the caches at their neighbors. In the latter case, when a user receives files from its neighbors, device-to-device(D2D) communication is performed. D2D communication underlaid with cellular networks is also a new paradigm for the upcoming wireless systems. By allowing a pair of adjacent D2D users to communicate directly, D2D communication can achieve higher throughput, better energy efficiency and lower traffic delay. In this work, we propose an efficient learning-based caching algorithm operating together with a non-parametric estimator to minimize the average transmission delay in D2D-enabled cellular networks. It is assumed that the system does not have any prior information regarding the popularity of the files, and the non-parametric estimator is aimed at learning the intensity function of the file requests. An algorithm is devised to determine the best <file,user> pairs that provide the best delay improvement in each loop to form a caching policy with very low transmission delay and high throughput. This algorithm is also extended to address a more general scenario, in which the distributions of fading coefficients and values of system parameters potentially change over time. Via numerical results, the superiority of the proposed algorithm is verified by comparing it with a naive algorithm, in which all users simply cache their favorite files, and by comparing with a probabilistic algorithm, in which the users cache a file with a probability that is proportional to its popularity.