In recent years, significant progress has been made in the research of metamaterial perfect absorbers for on-demand design based on deep learning methods, and how to improve the generalization ability and prediction accuracy of network models in inverse design has been a hot topic of recent research. In this paper, we propose a fully connected neural network (RFC-NN) based on the residual principle applied to the inverse design of perfect absorbers. We design the RFC-NN model by applying the residual network structure commonly used on convolutional neural networks to a fully connected neural network, and the regression coefficients of the predicted structural parameters and the corresponding absorption spectra in the inverse design are 0.988 and 0.923, respectively, which have better prediction performance and generalization ability than the ordinary fully connected neural network (FC-NN), tandem neural network (TNN), and one-dimensional residual convolutional neural network (1D-Resnet). Then, we successfully designed the metamaterial perfect absorber with an absorption bandwidth (the spectral range where the absorptivity is greater than 90%) of 1935 nm using the trained RFC-NN model, which corresponds to an average absorptivity of 93.70%. Meanwhile, we use the analysis method of the Pearson correlation coefficient to improve the accuracy of the RFC-NN model after inverse design. Our proposed design method proves to be very effective and can also be applied to the design of other types of functional nanophotonic devices.