This study aims to probe how children with and without autism spectrum disorders (ASD) attribute false belief to a social robot and predict its action accordingly. Twenty 5- to 7-year-old children with ASD and 20 age- and 10-matched typically developing (TD) children participated in two false belief tasks adapted for robot settings (change-of-location task and the unexpected-contents task). The results showed that most TD children are capable of attributing false belief to the social robot, that is, they could infer higher level mental states in robots, which extends our understanding in TD children's perception and cognition on social robots. Conversely, children with ASD still show difficulty in interpreting robots' mental states compared to their TD peers, which would greatly interfere with their interactions and communications with social robots and might impact on efficiency of robot-based intervention and education approaches. This group difference in attributing false belief to social robots could not be explained by the different perception and categorization of the robot. Our study implies that although children with ASD appear to be highly attracted by social robots, they still have difficulty in understanding mental states when socially interacting with robots, which should be taken into consideration when designing the robot-based intervention approach targeting to improve social behaviors of ASD.