  In this work we study the deflection and gravitational lensing of null and
timelike signals in the Kiselev spacetime in the weak field limit, to
investigate the effects of the equation of state parameter $\omega$ and the
matter amount parameter $\alpha$. In doing this, we extend a perturbative
method previously developed for asymptotically flat spacetimes whose metric
functions have integer-power asymptotic expansions to the case that may or may
not be asymptotically flat but with non-integer power expansions. It is found
that in the asymptotically flat case ($-1/3<\omega<0$) the deflection angles
are expressable as quasi-power series of the dimensionless quantities
$M/b,~b/r_{s,d}$ and $\alpha/M^{1+3\omega}$ where $M,~b,~r_{s,d}$ are
respectively the lens mass, impact parameter and source/detector radius. A
similar series exists for the non-asymptotically flat case of
($-1<\omega<-1/3$), but with the closest radius $r_0$ replacing $b$. In the
asymptotically flat (or non-flat) case, the increase of $\alpha$ or decrease of
$\omega$ will increase (or increase) the deflection angle. Since the obtained
deflection angles naturally take into account the finite distance effect of the
source and the detector, we can establish an exact gravitational lensing
equation, from which the apparent angles of the images and their magnifications
are solved. It is found that generally for the asymptotically flat case,
increasing $\alpha$ or decreasing $\omega$ will increase the apparent angles of
the images. While for the non-asymptotically flat case, increasing $\alpha$ or
$\omega$ will both lead to smaller apparent angles.
