It was found that the dark matter (DM) in the intermediate-mass-ratio-inspiral (IMRI) system has a significant enhancement effect on the orbital eccentricity of the stellar massive compact object, such as a black hole (BH), which may be tested by space-based gravitational wave (GW) detectors including LISA, Taiji and Tianqin in future observations citep{2019PhRvD.100d3013Y}. In this paper, we will study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses. Our results are as follows: $(1)$ in terms of the general DM spike distribution, the enhancement of the eccentricity is basically consistent with the power-law profile, which indicates that it is reasonable to adopt the power-law profile; $(2)$ in the presence of DM spike, the different masses of the center BH will affect the eccentricity, which provides a new way for us to detect the BHs mass; $(3)$ considering the change of the eccentricity in the presence and absence of DM spike, we find that it is possible to distinguish DM models by measuring the eccentricity at the scale of about $10^{5} GM/c^{2}$.
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