Nowadays, social robots have become human's important companions. The anthropomorphic features of robots, which are important in building natural user experience and trustable human-robot partnership, have attracted increasing attention. Among these features, eyes attract most audience's attention and are particularly important. This study aims to investigate the influence of robot eye design on users’ trustworthiness perception. Specifically, a simulation robot model was developed. Three sets of experiments involving sixty-six participants were conducted to investigate the effects of (i) visual complexity of eye design, (ii) blink rate, and (iii) gaze aversion of social robots on users’ perceived trustworthiness. Results indicate that high visual complexity and gaze aversion lead to higher perceived trustworthiness and reveal a positive correlation between the perceived anthropomorphic effect of eye design and users’ perceived trust, while a non-significant effect of blink rate has been found. Preliminary suggestions are provided for the design of social robots in future works.