In this paper, we propose an adaptive encoding method of fixed codebook in CELP coders and implement an adaptive fixed code exited linear prediction(AF-CELP) speech coder. AF-CELP exploits the fact that the fixed codebook contribution to speech signal is also periodic like the adaptive codebook (or pitch filter) contribution. By modeling the fixed code book with the pitch lag and the gain from the adaptive codebook, AF-CELP can be implemented at low bit rates as well as low complexity. Listening tests show that a 6.4 kbit/s AF-CELP has a comparable quality to the 8 kbit/s CS-ACELP in background noise conditions.