This paper investigates an inverse design method of acoustic programmable metamaterial beams based on deep learning. A theoretical model of programmable metamaterial beams is derived using the spectral element method to calculate the flexural wave propagation characteristic of the metastructure. Further, the vibration transmission characteristics of acoustic metamaterial beams are predicted, and the on-demand inverse design of programmable metamaterial beams is realized by constructing a fully connected deep-learning neural network model. The forward prediction and reverse design network models are verified using the autoencoder neural network model. Results show that the predicted value of the autoencoder neural network structure is in good agreement with the target value, which indicates the feasibility of the on-demand design method of programmable metamaterials based on deep learning. The intelligent design method could be potentially utilized in fast and efficient metamaterial design for low-frequency vibration isolation in engineering structures.