Optical scanning holography (OSH) records a three-dimensional object into a two-dimensional hologram through two-dimensional optical scanning. The recovery of sectional images from the hologram, termed as an inverse problem, has been previously implemented by conventional methods as well as the use of l₂ norm. However, conventional methods require time consuming processing of section by section without eliminating the defocus noise and the l₂ norm method often suffers from the drawback of over-smoothing. Moreover, these methods require the whole hologram data (real and imaginary parts) to eliminate the twin image noise, whose computation complexity and the sophisticated post-processing are far from desirable. To handle these difficulties, an adaptively iterative shrinkage-thresholding (AIST) algorithm, characterized by fast computation and adaptive iteration, is proposed in this paper. Using only a half hologram data, the proposed method obtained satisfied on-axis reconstruction free of twin image noise. The experiments of multi-planar reconstruction and improvement of depth of focus further validate the feasibility and flexibility of our proposed AIST algorithm.