Great progress has been made in modulating flexural waves by elastic metasurfaces. Most of the proposed elastic metasurfaces suffer from chromatic aberration, limited in a narrow bandwidth around the designed frequency. In this paper, overcoming the chromatic aberration, an ultra-broadband achromatic meta-slab (UAM) with subunits of gradient thickness is proposed to realize the refraction angle unchanged with the incident frequency. Based on the phase compensation principle, wavelength-dependent phase shifts for the UAM that realize achromaticity are obtained. In order to verify the effectiveness of the theoretical design, the transmitted wavefields are solved according to the phased array theory, and the results correspond with those obtained by the finite element (FE) simulations and experiments, which show that the refraction angle is unchanged for incident frequencies from 2 kHz to 8 kHz. Besides, the UAM is extended into a periodic meta-slab, and multifrequency achromaticity is realized. Our designed meta-slabs overcome the chromatic aberration by simple configurations, which have significance in the applications of vibration control, vibrational energy harvesting, and health monitoring.