When an input soliton pass through an optical amplifier, the soliton is boosted along together with the noise signal, and a random variation in the arrival time, called the Gordon-Haus effect, is induced. By the use of programmed chirp and a continuous dispersion profile, as envisaged by Kumar and Hasegawa, it is possible to produce a soliton like pulse called the quasi-soliton. This kind of pulse needs less peak power than the soliton and reduces the soliton-soliton interaction while keeps the benefits of optical solitons. Based on the results obtained by Kumar and Lederer for the Gordon-Haus effect on dispersion managed systems, we studied the influence of this effect in the quasi-soliton propagation. We have obtained an analytical solution for the mean square frequency shift. The expression obtained depends on the dispersion map parameters and the amplifier spacing. The results are shown for different values of the initial chirp.