In this paper, the SNR estimation error of Decision Directed SNR estimation method in AWGN is investigated, which uses samples received in reference decision region. In communication system receiver, when SNR estimation scheme using error vectors between ideal sample points and received sample points of reference region is adopted, the samples contain incorrectly received samples due to AWGN. Consequently, the mean of estimated reference constellation point is shifted and Decision Directed SNR estimation is inaccurately performed. These effects are explained by modified probability density function and difference between actual SNR and estimated SNR is theoretically derived and quantatively analyzed. It is proved that SNR estimation error obtained through computer simulation is matched up with derived one, and SNR estimation performance is enhanced significantly by adopting suggested correction scheme.