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 root s = 3000 GeV and integrated luminosity L = 5000 fb(-1) for the Compton backscattered initial photons. In particular, our limits are stronger than recently obtained bounds for the ALP production in the light-by-light scattering at the LHC.