Triply periodic minimal surfaces (TPMS) are engineered structures with controllable geometric topologies and excellent mechanical properties. However, traditional TPMS design methods are limited by their few adjustable parameters, which typically only allow optimization of shape and thickness, hindering performance enhancement. Hence, this paper proposes a novel reinforced TPMS design method based on isogeometric topology optimization to exploit the performance advantages fully. The design method improves performance by expanding the optimization space and increasing the design degrees of freedom through the double offset strategy. The isogeometric topology optimization for complex TPMS surface achieves model consistency, high accuracy and high efficiency in structural design. Finally, this reinforced design method is applied to the classical TPMS unit cells and numerical simulations of the reinforced unit cells are performed. By introducing a more flexible design domain and applying isogeometric topology optimization, our approach significantly improves the mechanical performance of TPMS structures, including stiffness, strength, and energy absorption. The key contribution of this work lies in its ability to overcome the limitations of traditional TPMS design, enabling a wider range of design possibilities and superior mechanical properties.