Due to the high-dimensional characteristics of photon orbital angular momentum (OAM), a beam can carry multiple OAMs simultaneously thus forming an OAM comb, which has been proved to show significant potential in both classical and quantum photonics. Tailoring broadband OAM combs on demand in a fast and accurate manner is a crucial basis for their application in advanced scenarios. However, obtaining phase-only gratings for the generation of arbitrary desired OAM combs still poses challenges. In this paper, we propose a multi-scale fusion learning U-shaped neural network that encodes a phase-only hologram for tailoring broadband OAM combs on-demand. Proof-of-principle experiments demonstrate that our scheme achieves fast computational speed, high modulation precision, and high manipulation dimensionality, with a mode range of $-75$ to $+75$, an average root mean square error of 0.0037, and a fidelity of 85.01%, all achieved in about 30 ms. Furthermore, we utilize the tailored broadband OAM combs in conducting optical convolution calculation, enabling vector convolution for arbitrary discrete functions, showcasing the extended capability of our proposal. This work opens, to our knowledge, new insight for on-demand tailoring of broadband OAM combs, paving the way for further advancements in high-dimensional OAM-based applications.