  In this work, the neutral Higgs boson pair production is analyzed at Compact
Linear Collider (CLIC) to be operating at center of mass energies
$\sqrt{s}$=1400 GeV (stage 2) and $\sqrt{s}$=3000 GeV (stage 3). The Higgs
bosons to be searched for are neutral CP-even (H) and CP-odd (A) within the
framework of two Higgs doublet model (2HDM) in the mass range 300 < mH/A < 1000
GeV. All types of the CP-conserving model are studied and the signal
observability is evaluated taking into account the main SM background processes
like ZZ, tt and the SM-like Higgs boson associated production (hZ). Results are
presented for a set of model parameters and Higgs boson masses in terms of
signal distributions over the background as well as the integrated luminosity
needed for 5{\sigma} discovery. It is shown that the heavy mass region is well
observable at CLIC in types 3 (flipped) and 4 (lepton-specific) in the regions
not excluded by LHC so far, while in type 1 the signal observation is
challenging due to the large jet multiplicity in the tt final state.
