We demonstrate both experimentally and theoretically the trapping and guiding of a weak signal pulse via a self-accelerating Airy pulse. This is achieved by launching the Airy pulse in the anomalous dispersion regime of an optical fiber, thereby inducing a gravity-like potential that can compel the signal pulse in the normal dispersion regime to undergo co-acceleration. Such guiding pulse by pulse can be controlled at ease simply by altering the acceleration conditions of the Airy pulse. Furthermore, the guided signal can be featured with either single or double peaks, which is explained by using the theory of fundamental and second-order quasi-modes associated with the gravity-like potential. Our work represents, to our knowledge, the first demonstration of pulse guiding in the anomalous dispersion regime of any self-accelerating pulse.