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Biodegradable materials have demonstrated promising potential for the treatment of bone fractures. Therefore, it is crucial to design biodegradable composites considering the degradation effect. Accordingly, to realize a composite material with controlled stiffness at the bone repair stage, this study introduces a novel topological optimization technique for the material layout design in microstructure, considering material degradation. In this approach, two sets of variables are adopted: a density field that defines the material layout, which is also the design variable, and a time field that determines the effect of material degradation on composite material properties. A continuous degradation update formula is proposed by integrating the Heaviside function and the Kreisselmeier–Steinhauser function to guarantee its derivability. The objective of this study was to maximize the material stiffness in some fixed time steps under a specified volume fraction. The sensitivity of the aforementioned objective relative to the design variable was deduced by considering the material degradation over time. The proposed design approach was demonstrated with several design examples, considering different degradable interface boundary conditions. Furthermore, the obtained results were compared with the results obtained without considering material degradation, thereby verifying the effectiveness of the proposed method.