A cascaded deep learning network model with physically consistent constraints was proposed for the modeling and design of terahertz metasurface biosensors. In this model, key resonance parameters, including resonance frequency, full width at half maximum, and quality factor, were explicitly treated as network outputs, and physically consistent constraints were imposed during training to ensure that the predictions obey fundamental resonance physics. Numerical results showed that the proposed model exhibited good convergence behavior and reliable prediction accuracy for the key resonance parameters. Based on the proposed model, a terahertz metasurface biosensor was designed and experimentally validated. The measured spectral response agreed well with the theoretical prediction, and trace detection of homocysteine molecules was successfully achieved. These results demonstrate that the proposed approach provides an effective modeling method for reliable and interpretable design of terahertz metasurface biosensors.