This article presents a novel variable-stiffness flexible manipulator for minimally invasive surgery. Each module of the proposed manipulator contains a variable-stiffness mechanism actuated by proactive deformation of shape memory alloy. Due to low driving current, apparent mechanical deformation, suitable phase transformation temperature and biocompatibility of shape memory alloy wire actuation, it is well suited for the manipulator applied in minimally invasive surgery, where variable stiffness is urgently required. In this article, the conceptual design, elastic modulus model, thermo-electric model, stiffness controlling method and finite element method simulation for a single module of the proposed variable-stiffness flexible manipulator are presented. Moreover, the memory shape setting experiment of shape memory alloy wire and fabrication of the single module are carried out. Finally, stiffness characterizations of the mechanism and the single module are studied separately, theoretically and experimentally.