Intelligent reflecting surface (IRS) operating in the terahertz (THz) band has recently gained considerable interest due to its high spectrum bandwidth. Due to the exploitation of large scale of IRS, there is a high probability that the transceivers will be situated within the near-field region of the IRS. Thus, the near-field beam split effect poses a major challenge for the design of wideband IRS beamforming, which causes the radiation beam to deviate from its intended location, leading to significant gain losses and limiting the efficient use of available bandwidths. While delay-based IRS has emerged as a potential solution, current beamforming schemes generally assume unbounded range time delays (TDs). In this letter, we first investigate the near-field beam split issue at the IRS. Then, we extend the piece-wise far-field model to the IRS, based on which, a double-layer delta-delay (DLDD) IRS beamforming scheme is proposed. Specifically, we employ an element-grouping strategy and the TD imposed on each sub-surface of IRS is achieved by a series of TD modules. This method significantly reduces the required range of TDs. Numerical results show that the proposed DLDD IRS beamforming scheme can effectively mitigate the near-field beam split and achieve near-optimal performance.