  Three dimensional wormholes are global solutions of Einstein-Hilbert action.
These space-times which are quotients of a part of global AdS$_{3}$ have
multiple asymptotic regions, each with conformal boundary
$S^{1}\times\mathbb{R}$, and separated from each other by horizons. Each outer
region is isometric to BTZ black hole, and behind the horizons, there is a
complicated topology. The main virtue of these geometries is that they are dual
to known CFT states. In this paper, we evaluate the full time dependence of
holographic complexity for the simplest case of $ 2+1 $ dimensional Lorentzian
wormhole spacetime, which has three asymptotic AdS boundaries, using the
complexity equals volume (CV) conjecture. We conclude that the growth of
complexity is non-linear and saturates at late times.
