Origami structures have extensive applications in multiple scientific and engineering fields, such as smart structures, sensors, autonomous robotics, and tissue-engineering metamaterials. Origami-inspired mechanical metamaterials’ performance and behavior are intricately linked to their structural design. Square-twist origami, with its unique bistable mechanical properties, has 16 crease patterns (4 independent), but there is a lack of theoretical and quantitative analysis methods for Type 1, resulting in high-cost structural design. In this paper, a mechanical metamaterial structure inspired by square-twist origami is proposed. A Python-ABAQUS framework is used to generate datasets for deep learning training. A deep neural network (DNN) model is built to predict the maximum strain energy of the structure. The results show that the DNN model has a high prediction accuracy (accuracy of 0.95), which can effectively reduce the calculation time compared with traditional methods. The proposed framework can be used to predict structures that meet specific engineering requirements, providing a new way for the design of origami-inspired mechanical metamaterial structures.