  In this work we are about to investigate the effects of quintessence dark
energy on evolution of the computational complexity relating to the AdS/CFT
correspondence. We use $"complexity=action"$ conjecture for a charged AdS black
hole surrounded by the dark energy at the quintessence regime.
  Then we try to find some conditions on the quintessence parameters where the
Lloyd bound is satisfied in presence of affects of the quintessence dark energy
on the complexity growth at the late time approximations. We compare late time
approximation of the action growth by perturbed geometry in small limits of
shift function.
  Actually we investigate the evolution of complexity when thermofield double
state on the boundaries is perturbed by local operator corresponding to a shock
wave geometry as holographically. Furthermore we seek spread of local shock
wave on the black hole horizon in presence of the quintessence dark energy.
