We propose a hybrid model based on long short-term memory (LSTM) and refractive index (RI) fault detection for the industrial terpolymerization process. This LSTM-based hybrid model integrates a first-principles model with LSTM to predict both the composition of the terpolymer and the concentration of monomers. Within this hybrid framework, the LSTM predicts the conversion using process variables, while the terpolymer composition is calculated using the first-principles model and the predicted conversion. The error for monomer composition prediction of the proposed hybrid model was reduced by 20% compared to the data-only model when the composition change exists. In addition, the RI fault detection is conducted using the augmented data by the hybrid model, and the F1 score increased by 5% compared to the model predicted using process variables alone.