In this paper, the generation and propagation of self-similar pulses in an Er-doped mode-locked fiber laser based on saturable absorber (SA) are numerically investigated. Research results indicate that by using a germanium rod to compensate the cavity dispersion, the intracavity pulse of an erbium-doped fluoride fiber laser based on SA mode-locking can support self-similar pulses evolution when the net dispersion of the cavity is in the range of 0.020-0.048 ps². Keeping the net dispersion of the cavity with 0.03 ps², ideal parabolic pulse with a pulse width of 19.7 ps, a peak power of 630 W, and a pulse energy of 12.4 nJ is obtained. To further optimize the output properties of the laser, the effects of small signal gain and gain saturated energy of the gain fiber, as well as the modulation depth and saturated power of the SA on the pulse output properties are studied in detail, which provides reference for the design of self-similar mode-locked Er-doped fluoride fiber lasers.