A large body of experimental research has provided empirical support for the link between cognitive ability and attitudes towards risk. However, the findings have not been consistently confirmed. In this study, we try to investigate whether the relationship between cognitive ability and risk aversion is sensitive to the availability of the safe option condition—the availability of a riskless alternative in which a positive amount of money can be obtained with certainty. The subjects (n = 112) were divided into high- (n = 42) and low (n = 40) cognitive abilities according to their scores on Raven's Colored Progressive Matrices Test (RCPM). We conducted a laboratory experiment in which subjects with two groups made both safe and unsafe risky decisions using the Bomb Risk Elicitation Task (BRET). The experimental findings revealed that the relationship between cognitive ability and risk aversion is insensitive to safe option conditions as the high cognitive ability group performed more riskier than the low ability group even with the availability of riskless alternatives. Moreover, introducing the riskless alternative makes both high- and low-cognitive ability groups more risk-tolerant in both high- and low-risk-loving domains.