Soft robots exhibit significant advantages over traditional rigid robots in flexible grasping, complex environment operations, and rehabilitation medicine due to their superior adaptability and safety. However, the highly nonlinear deformation of soft materials makes the precise control of continuous large deformations a formidable challenge. Traditional analytical models and parametric design methods are often constrained by oversimplified kinematic assumptions and predefined topological templates, which restrict the design space and hinder the accurate realization of complex target configurations. This work proposes a topology optimization inverse design method to enable soft robots to accurately approximate target shapes. The Solid Isotropic Material with Penalization (SIMP) method is employed to optimize the spatial distribution of soft and stiff materials, thereby regulating deformation modes by modulating the local stiffness of the structure. To enhance computational efficiency, the Equivalent Static Loads (ESL) method is incorporated to transform the complex large-deformation nonlinear optimization into linear static problems, effectively bypassing expensive nonlinear sensitivity analysis. Compared with traditional methods, the proposed approach leverages a larger scale of design degrees of freedom, resulting in superior control precision. Numerical examples demonstrate that the method can precisely match target displacement fields, with corresponding experimental tests further verifying its feasibility and accuracy.