Recent research has suggested the importance of part-based information in face recognition in addition to global, whole-face information. Nevertheless, face drawing experience was reported to enhance selective attention to the eyes but did not improve face recognition performance, leading to speculations about limited plasticity in adult face recognition. Here we examined the mechanism underlying the limited advantage of face drawing experience in face recognition through the Eye Movement analysis with Hidden Markov Models (EMHMM) approach. We found that portrait artists showed more eyes-focused eye movement patterns and outperformed novices in face matching, and participants' drawing rating was correlated with both eye movement pattern and performance. In contrast, portrait artists did not outperform novices and did not differ from novices in eye movement pattern in either the face recognition or part-whole tasks, although the eyes-focused pattern was associated with better recognition performance and longer response times in the whole condition relative to the part condition. Interestingly, in contrast to the face recognition and part-whole tasks, participants' performance in face matching was predicted by their drawing rating but not eye movement pattern. These results suggested that artists' advantage in face processing is specific to tasks similar to their drawing experience such as face matching, and may be related to their better ability in extracting identity-invariant information between two faces rather than more eyes-focused eye movement patterns.