Fast Radio Bursts (FRBs) have emerged as one of the most intriguing and enigmatic phenomena in the field of radio astronomy. The key of current related research is to obtain enough FRB signals. Computer-aided search is necessary for that task. Considering the scarcity of FRB signals and massive observation data, the main challenge is about searching speed, accuracy and recall. in this paper, we propose a new FRB search method based on Commensal Radio Astronomy FAST Survey (CRAFTS) data. The CRAFTS drift survey data provide extensive sky coverage and high sensitivity, which significantly enhance the probability of detecting transient signals like FRBs. The search process is separated into two stages on the knowledge of the FRB signal with the structural isomorphism, while a different deep learning model is adopted in each stage. To evaluate the proposed method, FRB signal data sets based on FAST observation data are developed combining simulation FRB signals and real FRB signals. Compared with the benchmark method, the proposed method F-score achieved 0.951, and the associated recall achieved 0.936. The method has been applied to search for FRB signals in raw FAST data. The code and data sets used in the paper are available at github.com/aoxipo.