Code excited Linear Prediction(CELP) vocoder exhibits good performance at data rates below 4.8 kbps. The major drawback of CELP type coders is their large amount of computation. In this paper, we propose a new pitch searching method that preseves the quality of the CELP vodocer reducing computational complexity. The basic idea is that pregrasps preliminary pitches about signal and performs pitch search only about the preliminary pitches. Applying the proposed method to the CELP vocoder, we can reduce complexity about 90% in th pitch search.