Most of the schemes for generating isolated attosecond pulses (IAP) are sensitive to the carrier-envelope phase (CEP) of the driving lasers.We propose a scheme for generating IAP using two-color counter-rotating circularly polarized (TCCRCP) laser pulses.The results demonstrate that the dependence of the IAP generation on CEP stability is largely reduced in this scheme.IAP can be generated at most of CEPs.Therefore,the experiment requirements become lower.