The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to T-;mu(mu nu) = lambda R-,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.