  We calculate the cosmological complexity under the framework of scalar
curvature perturbations for a K-essence model with constant potential. In
particular, the squeezed quantum states are defined by acting a two-mode
squeezed operator which is characterized by squeezing parameters $r_k$ and
$\phi_k$ on vacuum state. The evolution of these squeezing parameters are
governed by the $Schr\ddot{o}dinger$ equation, in which the Hamiltonian
operator is derived from the cosmological perturbative action. With aid of the
solutions of $r_k$ and $\phi_k$, one can calculate the quantum circuit
complexity between unsqueezed vacuum state and squeezed quantum states via the
wave-function approach. One advantage of K-essence is that it allows us to
explore the effects of varied sound speeds on evolution of cosmological
complexity. Besides, this model also provides a way for us to distinguish the
different cosmological phases by extracting some basic informations, like the
scrambling time and Lyapunov exponent etc, from the evolution of cosmological
complexity.
