This letter proposes a convolutional neural network (CNN)-based adaptive controller wtih three notable features: 1) it determines control input directly from historical sensor data (in an end-to-end process); 2) it learns the desired control policy during real-time implementation without using a pretrained network (in an online adaptive manner); and 3) the asymptotic tracking error convergence is proven during the learning process (to deliver a stability guarantee). An adaptive law for learning the desired control policy is derived using the gradient descent optimization method, and its stability is analyzed based on the Lyapunov approach. A simulation study using a control-affine nonlinear system demonstrated that the proposed controller exhibits these features, and its performance can be tuned by manipulating the design parameters. In addition, it is shown that the proposed controller has a superior tracking performance to that of a deep neural network (DNN)-based adaptive controller.