Wrinkling behavior of sheet metal by inappropriate process parameters and the resultant variation of thickness and microstructure during incremental sheet forming (ISF) have significant impact on forming stability and geometric profile. The wrinkling-related mechanism is yet to be well understood, which make it difficult to effectively control wrinkling defects during ISF. In the present work, the wrinkling behavior and related mechanism of a typical annular grooved panel are investigated during a novel flexible free ISF process. Experiments demonstrate that during this ISF process, the sheet material sequentially undergoes 4 deformation modes: contacting state under plane strain condition, contracting state with only elastic deflection, thickening state under uniaxial compression condition, and wrinkling state where the circumferential compressive stress exceeds the critical wrinkling stress. The evolution of these deformation modes is dominantly caused by the increasing of edge contraction and circumferential stress, which are induced by the bending moment from the forming tool and auxiliary sheets. Based on the mechanism, an analytical model is developed to predict the wrinkling behavior, by which the corresponded sheet thickness, bending moment, circumferential compressive stress and critical wrinkling stress during the wrinkling process could be comprehensively calculated. Experimental results validate that the analytical model can accurately predict the wrinkling behavior under different process parameters, material properties and auxiliary sheet materials. Through microstructural characterization, numerical simulation and analytical modeling, the influence of process parameter and material property on wrinkling behavior is systematically investigated, along with the variation of sheet thickness and microstructure under different wrinkling modes. This work enhance a deep understanding of wrinkling behavior during ISF process, thereby providing effective methods for process optimization and quality improvement.