To meet the growing demand for high data rates, cellular systems are expected to evolve towards higher carrier frequencies and larger antenna arrays, but conventional phased arrays face challenges in supporting such a prospection due to their excessive power consumption induced by numerous phase shifters required. Reconfigurable Refractive Surface (RRS) is an energy efficient solution to address this issue without relying on phase shifters. However, the increased radiation aperture size extends the range of the Fresnel region, leading the users to lie in the near-field zone. Moreover, given the wideband communications in higher frequency bands, we cannot ignore the frequency selectivity of the RRS. These two effects collectively exacerbate the beam-split issue, where different frequency components fail to converge on the user simultaneously, and finally result in a degradation of the data rate. In this paper, we investigate an RRS-based wideband near-field multi-user communication system. Unlike most existing studies on wideband communications, which consider the beam-split effect only with the near-field condition, we study the beam-split effect under the influence of both the near-field condition and the frequency selectivity of the RRS. To mitigate the beam-split effect, we propose a Delayed-RRS structure, based on which a beamforming scheme is proposed to optimize the user's data rate. Through theoretical analysis and simulation results, we analyze the influence of the RRS's frequency selectivity, demonstrate the effectiveness of the proposed beamforming scheme, and reveal the importance of jointly considering the near-field condition and the frequency selectivity of RRS.