Trapped ions, under electromagnetic confinement and Coulomb repulsion, can behave as non-interacting particles in one-dimensional lattices. Here we explore analytically the possible effects regarding Anderson localization in a chain of trapped ions experiencing laser Bessel beams. Under an experimentally feasible condition, we predict an analytical form of the energy-dependent mobility edges, which is verified to be in good agreement with the exact numerical results except for the top band. Some other important properties regarding the phonon localization in the ion chain are also discussed both analytically and numerically. Our results are relevant to experimental observation of localization–delocalization transition in the ion trap and helpful for deeper understanding of the rich phenomena due to long-range phonon hopping.