Self-similarity is a relatively common natural phenomenon, which is also found in pulses transmitted in optical fibers. Self-similar pulses are parabolic pulses. In fiber amplifier, pulses can evolve into such parabolic pulses under the combined influence of gain, normal dispersion and nonlinearity. This is the definition of self-similar pulses in early research. When a pulses is transmitted under this condition, not only does the shape gradually evolve into a parabolic shape, but the shape of the pulse can be maintained, and the pulse width and power are amplified at the same time. The evolved self-similar pulse has a linear chirp curve, which can achieve long distance relative transmission without pulse splitting in the case of high power. Therefore, self-similar pulses are also applied to the mode-locked fiber laser. Although the fiber laser cavity is different from the fiber amplifier, the self-similar pulse in the cavity still has the characteristic of anti-splitting, which improves the output pulse energy of the mode-locked fiber laser. The gain fiber of the self-similar fiber laser also basically meets the generation requirements of the initial self-similar pulse, but these requirements are difficult to achieve for current mid-infrared fiber lasers. In the mid-infrared band, the fiber is usually in the anomalous dispersion region. If the wave guide dispersion and doped rare earth of the gain fibre are adjusted substantially, it will bring extreme difficulties to fiber fabrication. Self-similar pulse fiber lasers are mainly divided into passive self-similar fiber lasers and active self-similar fiber lasers. Active self-similar fiber lasers usually require spectral filtering, where the pulses in the cavity evolve into self-similar pulses in the gain fiber part. Therefore, the gain fiber of the active self-similar lasers must be normal dispersion, which is difficult to adapt to the gain fiber with anomalous dispersion in the mid-infrared band. In the passive self-similar fiber laser, the self-similar evolution is in the passive fiber with normal dispersion. Even if there is a passive fiber with anomalous dispersion in the laser cavity, the self-similar pulses can still be output as long as the net dispersion of the laser system is positive. Dispersion-managed fiber laser, usually specifically a dispersion-managed soliton fiber laser, is a laser with dispersion map structure, and also generally refers to all fiber lasers that control dispersion in the cavity. Whether the dispersion-managed cavity with anomalous dispersion gain fiber can become a passive self-similar fiber laser and output self-similar pulses with comparable quality should be further researched. For the sake of comparison, this paper, first systematically summarizes the historical evolution, classification system and respective characteristics of mode-locked fiber lasers with normal dispersion. Then, the dispersion-managed mode-locked fiber laser with anomalous dispersion gain fiber is studied by numerical simulation. Through the analysis of time domain shape, spectrum, pulse energy, pulse width and chirp curve linearity and comparison with several traditional self-similar pulse fiber lasers constructed by normal dispersion gain fibers with mirror dispersion characteristics, it is pointed out that the laser system completely conforms to the features of passive self-similar fiber laser, and can achieve the effect of traditional passive self-similar fiber laser constructed by normal dispersion gain fiber. The realizable range of self-similar pulse fiber lasers is expanded theoretically, which makes up for the theory deficiency of traditional self-similar pulse fiber lasers in this aspect. In addition, the influence of dispersion map, net dispersion in the cavity and dispersion compensation nonlinearity on the output pulse of the laser system is discussed in detail, which provides a new idea for generating higher quality ultrashort pulses in the mid-infrared band using anomalous dispersion gain fiber.