Shape-morphing systems have a wide range of application scenarios. Its potential for controlling transformation into arbitrary three-dimensional (3D) shapes needs to be realized. This study aimed to develop a novel programming control strategy. A flat sheet obtained by discretizing the curved surface with cross-structure units without in-plane strain interference can be deformed into an arbitrary 3D space surface model. The division of the deformable and central fixed parts of the cross-structure prevents deformation interference. Fused filament fabrication pre-programmed four-dimensional printing technology was used to control the deformable part transformation. The self-developed software performed the flattening, discretization, and optimization of the target surface to generate a printed plane model composed of a cross-structure. A self-developed slicing tool completed the printing process. The finite element simulation results of the sample model were consistent with those of the target surface. The experimental results of the model deformation confirmed the effectiveness and accuracy of the approach. The novel programming control strategy for printing arbitrarily complex 3D deformation systems exhibited high theoretical precision. Its universality promotes development of the shape-morphing system manufacturing field.