During the actual operation of the solid oxide fuel cell (SOFC), degradation is one of the most difficult technical problems to overcome. Predicting the degradation trend and estimating the remaining useful life (RUL) can effectively diagnose the potential failure and prolong the useful life of the fuel cell. To study the degradation trend of the SOFC under constant load conditions, a SOFC degradation model based on the ohmic area specific resistance (ASR) is presented first in this paper. Based on this model, a particle filter (PF) algorithm is proposed to predict the long-term degradation trend of the SOFC. The prediction performance of the PF is compared with that of the Kalman filter, which shows that the proposed algorithm is equipped with better accuracy and superiority. Furthermore, the RUL of the SOFC is estimated by using the obtained degradation prediction data. The results show that the model-based RUL estimation method has high accuracy, while the excellence of the PF algorithm for degradation trend prediction and RUL estimation is proven.