  We study the complexity of holographic superconductors
(Einstein-Maxwell-complex scalar actions in $d+1$ dimension) by the `complexity
= volume' (CV) conjecture. First, it seems that there is a universal property:
the superconducting phase always has a smaller complexity than the unstable
normal phase below the critical temperature, which is similar to a free energy.
We investigate the temperature dependence of the complexity. In the low
temperature limit, the complexity (of formation) scales as $T^\alpha$, where
$\alpha$ is a function of the complex scalar mass $m^2$, the $U(1)$ charge $q$,
and dimension $d$. In particular, for $m^2=0$, we find $\alpha=d-1$,
independent of $q$, which can be explained by the near horizon geometry of the
low temperature holographic superconductor. Next, we develop a general
numerical method to compute the time-dependent complexity by the CV conjecture.
By this method, we compute the time-dependent complexity of holographic
superconductors. In both normal and superconducting phase, the complexity
increases as time goes on and the growth rate saturates to a temperature
dependent constant. The higher the temperature is, the bigger the growth rate
is. However, the growth rates do not violate the Lloyd's bound in all cases and
saturate the Lloyd's bound in the high temperature limit at a late time.
