The lateral shifts of the wave reflected and transmitted from PT-symmetric one-dimensional multilayer-structures are investigated near the coherent-perfect-absorption (CPA)-laser point and the exceptional points. We predict that at the CPA-Laser point, the reflections from both sides and transmission as well as the related shifts are all very large, reaching their negative (or positive) maxima. Moreover, we show that although the reflections are direction-dependent in the PT-symmetric multilayer-structure, the related lateral shifts have same behaviors from both sides. Additionally, one may realize the reversal of the lateral shift through the suitable adjustment of the incident angle and the layer numbers. Numerical simulations for Gaussian incident beams are performed, and reasonable agreement between the theoretical results and numerical simulations is found.