  The virtual production of axion-like particles (ALPs) in the light-by-light
scattering at the CLIC collider is studied. Both differential and total cross
sections are calculated, assuming interaction of the ALP with photons via
CP-odd term in the Lagrangian. The 95\% C.L. exclusion regions for the ALP mass
and its coupling constant are given. By comparing our results with existing
collider bounds, we see that the ALP search at the CLIC has a great physics
potential of searching for the ALPs, especially, in the mass region 1 TeV --
2.4 TeV, with the collision energy $\sqrt{s} = 3000$ GeV and integrated
luminosity $L = 5000$ fb$^{-1}$ for the Compton backscattered initial photons.
In particular, our limits are stronger that recently obtained bounds for the
ALP production in the light-by-light scattering at the LHC.
