In order to speed up the process of optimizing design of metasurface absorbers, an improved design model for metasurface absorbers based on autoencoder (AE) and BiLSTM-Attention-FCN-Net (including bidirectional long-short-term memory network, attention mechanism, and fully-connection layer network) is proposed. The metasurface structural parameters can be input into the forward prediction network to predict the corresponding absorption spectra. Meantime, the metasurface structural parameters can be obtained by inputting the absorption spectra into the inverse prediction network. Specially, in the inverse prediction network, the bidirectional long-short-term memory (BiLSTM) network can effectively capture the context relationship between absorption spectral sequence data, and the attention mechanism can enhance the BiLSTM output sequence features, which highlight the critical feature information. After the training, the mean square error (MSE) value on the validation set of the reverse prediction network converges to 0.0046, R2 reaches 0.975, and our network can accurately predict the metasurface structure parameters within 1.5s with a maximum error of 0.03mm. Moreover, this model can achieve the optimal design of multi-band metasurface absorbers, including the single-band, dual-band, and three-band absorptions. The proposed method can also be extended to other types of metasurface optimization design.