The normal modes cannot be extracted even in the Pekeris waveguide when the source-receiver distance is very close. This paper introduces a normal mode extraction method based on a dedispersion transform (DDT) to solve this problem. The method presented here takes advantage of DDT, which is based on the waveguide invariant such that the dispersion associated with all of the normal modes is removed at the same time. After performing DDT on a signal received in the Pekeris waveguide, the waveform of resulting normal modes is very close to the source signal, each with different position and amplitude. Each normal mode can be extracted by determining its position and amplitude parameters by applying particle swarm optimization (PSO). The waveform of the extracted normal mode is simply the waveform of the source signal; the real waveform of the received normal mode can then be recovered by applying dispersion compensation to the source signal. The method presented needs only one receiver and is verified with experimental data