The all-normal-dispersion mode locked fiber laser can produce the dissipative soliton pulses because the laser can tolerate much more nonlinear phase shift than the other mode locked fiber lasers. Such large energy mode locked fiber lasers are excellent seed pulse sources for generating very large-energy ultrashort pulses with fiber chirped pulse amplification (CPA) systems. However, the spectral amplitude modulation carried by the dissipative soliton pulses will severely restrict the compressibility of the output pulses from the typical CPA system. Therefore, it is necessary to investigate and design a suitable CPA system for improving the compressibility of the output pulses according to the properties of dissipative solitons. In this paper, using the dissipative solitons generated by the all-normal-dispersion fiber laser with different spectral filter bandwidths as the input seed pulses, the compressible properties of the pulses for the CPA system with both the grating pair stretcher and the fiber stretcher are investigated. Our simulation results show that, for such a large-energy dissipative soliton seed pulse, when the grating pair stretcher is used in the CPA system, the spectral amplitude modulation of the seed pulse can be mapped to the temporal amplitude modulation by the stretcher, and amplified by the subsequent fiber amplifier, which introduces additional nonlinear phase, finally restricts the compressibility of the output pulses; when the normal-dispersion fiber stretcher is used, the interaction between the group velocity dispersion and the self-phase modulation can not only eliminate the influence of the modulated spectrum of the dissipative soliton on the compressible properties of the pulses, but also make it possible to evolve the pulse self-similarity in the fiber stretcher, and thus improve the compressibility of the output pulses of the CPA system. For the normal-dispersion fiber stretcher CPA system, the compressibility of the output pulses is mainly determined by the fiber stretcher length. If the fiber length is too short, the compressibility of the output pulses may be affected by the uncompleted self-similar evolution of the pulse, while the pulse compressibility is also restricted because the pulse spectral width may exceed the amplifier gain bandwidth due to the self-similar evolution process if the fiber length is too long. Moreover, for the dissipative soliton seed pulses, both the compressibility of the output pulses and the energy ratio of the main pulse to the total pulse for the CPA system with the fiber stretcher are better than those with the grating pair stretcher when the normal fiber stretcher length is suitably optimized.