  A black string is a solution of the four-dimensional general relativity in
cylindrical symmetric anti-de Sitter (AdS) spacetime pioneered by Lemos [6]. We
obtain an exact rotating black string surrounded by quintessence matter in
anti-de Sitter (AdS) spacetime and analyze its properties. The solution has an
additional parameter $N_q$ due to background quintessence matter and it also
depends on quintessence state parameter $w_q$. Our rotating solution
encompasses the Lemos black string \cite{Lemos:1994xp}, which can be recovered
in the absence of background matter ($N_q=0$). The special case of rotating
charged black string ($w_q=1/3$) has both Cauchy and event horizons. We find
that thermodynamic quantities mass, temperature, entropy and heat capacity get
corrected due to quintessence background. The counterterm method is utilized to
calculate the associated conserved quantities to conclude that the first law of
thermodynamics is satisfied. The cloud of strings background ($w_q= -1/3$) has
been included as a special case.
