Kiselev black hole possesses the two horizons, i.e. the inner horizon and outer horizon. In some cases, the so-called outer horizon of black hole is actually a cosmic horizon. In this paper, Kiselev space-time with black hole horizon and cosmic horizon is considered. The radius of black hole horizon and the radius of cosmic horizon are approximately obtained to be $r_{\rm B} \approx 2M \left[ 1 + \left(2M/{\lambda}\right)^{-(3w_{\rm {\rm q}}+1)} \right]$ and $r_{\rm C} \approx \lambda + \dfrac{2M} {3w_{\rm {\rm q}}+1}$ with $M \ll \lambda$ and $w_{\rm q}$ a parameter. The energy density of the Kiselev spacetime near the cosmic horizon is approximately proportional to $w_{\rm q}$ , so the energy densities with some different $ w_{\rm q}$ have the same order of magnitude in the range $-1 . Near the black hole horizon, it increases rapidly with the increase of $w_{\rm q}$ .　　The thermodynamic properties of the systems with black hole horizon and cosmic horizon as boundary are studied. The first law of thermodynamics for the two systems is given in a unified way. Similarly, Smarr relation for the mass of Kiselev black hole is also obtained. For $M \ll \lambda $ , the work done by the fluid on the cosmic horizon and the thermal energy flux flowing into the cosmic horizon of Kiselev spacetime are calculated approximately. In the range of $-1 < w_{\rm q} < - 1/3 $ , the thermal energy always flows out of the cosmic horizon. The work done by the fluid on the black hole horizon is much smaller than the change in the energy of black hole, $\Delta w_{\rm B} \ll \Delta r_{\rm B}$ . This indicates that the energy increase of black hole comes mainly from the thermal energy flowing into the black hole through its outer horizon. The problem of accreting the pressureless fluid into Kiselev black hole is discussed. One can find that there are the zero gravity surfaces between the black hole horizon and cosmic horizon of Kiselev spacetime, the radii of which increase with the decrease of $w_{\rm q}$ . For $w_{\rm q}=-\dfrac{2}{3}$ and $w_{\rm q}=-1$ , the accretion radii of Kiselev black hole are respectively determined to be $r_0 \approx 1.6 \times 10^{4}$ (l.y.) and $r_0 \approx 1.2 \times 10^{6}$ (l.y.). On condition that the accretion energy density is proportional to the background energy density, $\rho_{\rm {mB}} = \eta_{\rm B} \rho_{\rm B}$ with $\eta_{\rm B}$ being a proportionality coefficient, the accretion rate of Kiselev black hole is given as $\chi_{\rm B} = - \dfrac{3 \eta_{\rm B} w_{\rm q}} {2} \left(\dfrac{2M}{\lambda}\right)^{-(3w_{\rm q} + 1)}$ . For $w_{\rm q}= - 2/3 $ , the accretion rate of the black hole takes its maximum $\chi_{\rm max} \approx 1.2 \times 10^{- 6} \eta_{\rm B} $ ; for $w_{\rm q}= - 1$ , the accretion rate takes its minimum $\chi_ {\rm {min}} \approx 1.2 \times 10 ^ {-8} \eta_{\rm B} $ . On the assumption that $\eta_{\rm B}$ changes slowly enough with $w_{\rm q}$ , the accretion rate of Kiselev black hole increases with the increase of $w_{\rm q}$ .