The Talbot self-imaging effect is mostly present in the forms of space or time, or in the frequency domain by the Fourier duality. Here, we disclose a new spectral Talbot effect arising in optical orbital angular momentum (OAM) modes. The effect occurs in the context of petal-like beams, which are typically constructed from a number of in-phase equidistant OAM modes with at least one void mode in between. When illuminating such beams on phase masks that are azimuthally modulated with Talbot phases, the initial OAM modes are self-imaged to create new OAM modes, meanwhile preserving the initial OAM spectral profile. Such a phenomenon is theoretically predicted, and a close analogy is drawn with the spectral Talbot effect of frequency combs. The prediction is also experimentally confirmed by observing versatile spectral self-imaging on various optical petal-like beams. 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).