Based on the transverse-longitudinal mapping of Bessel beams, we propose a simple method to construct a self-similar Bessel-like beam whose transverse profile maintains a stretched form during propagation. Specifically, the propagating-variant width of this beam can be flexibly predesigned. We experimentally demonstrate three types of self-similar Bessel-like beams whose width variations are linear, piecewise, and period functions of propagation distance, respectively. The experimental results match well with the theoretical predictions. We also demonstrate that our approach enables the generation of self-similar higher-order vortex Bessel-like beams.