Relay selection is a crucial method that can improve the spectrum efficiency and converge performance of relay assisted (RA) network. However, most of the existing research about relay selection did not consider the effect of imperfect channel state information (CSI) and the CSI obtaining cost. Few of the study about the relay selection with imperfect CSI focused mainly on the decode-and-forward (DF) protocol. In order to overcome these shortage, a sequence relay selection strategy (SRSS) for the amplify-and-forward (AF) RA network is proposed and analyzed in this paper. Furthermore, in order to make SRSS more practical, the optimal stopping (OS) theory is investigated to work with SRSS. Numerical results indicate that the performance of SRSS with OS theory can achieve the upper bound performance of SRSS effectively.