  The Rastall gravity is the modified Einstein general relativity, in which the
energy-momentum conservation law is generalized to $T^{\mu\nu}_{~~;\mu}=\lambda
R^{,\nu}$. In this work, we derive the Kerr-Newman-AdS (KN-AdS) black hole
solutions surrounded by the perfect fluid matter in the Rastall gravity using
the Newman-Janis method and Mathematica package. We then discuss the black hole
properties surrounded by two kinds of specific perfect fluid matter, the dark
energy ($\omega=-2/3$) and the perfect fluid dark matter ($\omega=-1/3$).
Firstly, the Rastall parameter $\kappa\lambda$ could be constrained by the weak
energy condition and strong energy condition. Secondly, by analyzing the number
of roots in the horizon equation, we get the range of the perfect fluid matter
intensity $\alpha$, which depends on the black hole mass $M$ and the Rastall
parameter $\kappa\lambda$. Thirdly, we study the influence of the perfect fluid
dark matter and dark energy on the ergosphere. We find that the perfect fluid
dark matter has significant effects on the ergosphere size, while the dark
energy has smaller effects. Finally, we find that the perfect fluid matter does
not change the singularity of the black hole. Furthermore, we investigate the
rotation velocity in the equatorial plane for the KN-AdS black hole with dark
energy and perfect fluid dark matter. We propose that the rotation curve
diversity in Low Surface Brightness galaxies could be explained in the
framework of the Rastall gravity when both the perfect fluid dark matter halo
and the baryon disk are taken into account.
