Constructing a computing circuit in three dimensions (3D) is a necessary step to enable the massive connections and efficient communications required in complex neural networks. 3D circuits based on conventional complementary metal–oxide–semiconductor transistors are, however, difficult to build because of challenges involved in growing or stacking multilayer single-crystalline silicon channels. Here we report a 3D circuit composed of eight layers of monolithically integrated memristive devices. The vertically aligned input and output electrodes in our 3D structure make it possible to directly map and implement complex neural networks. As a proof-of-concept demonstration, we programmed parallelly operated kernels into the 3D array, implemented a convolutional neural network and achieved software-comparable accuracy in recognizing handwritten digits from the Modified National Institute of Standard and Technology database. We also demonstrated the edge detection of moving objects in videos by applying groups of Prewitt filters in the 3D array to process pixels in parallel.