This Letter presents a structure-embedding network (SEmNet) to predict the transmission spectrum of a multilayer deep etched grating (MDEG). Spectral prediction is an important procedure in the MDEG design process. Existing approaches based on deep neural networks have been applied to spectral prediction to improve the design efficiency of similar devices, such as nanoparticles and metasurfaces. Due to a dimensionality mismatch between a structure parameter vector and the transmission spectrum vector, however, the prediction accuracy decreases. The proposed SEmNet can overcome the dimensionality mismatch problem of deep neural networks to increase the accuracy of predicting the transmission spectrum of an MDEG. SEmNet consists of a structure-embedding module and a deep neural network. The structure-embedding module increases the dimensionality of the structure parameter vector with a learnable matrix. The augmented structure parameter vector then becomes the input to the deep neural network to predict the transmission spectrum of the MDEG. Experiment results demonstrate that the proposed SEmNet improves the prediction accuracy of the transmission spectrum in comparison with the state-of-the-art approaches.