We discuss bounds from perturbative unitarity in a composite two Higgs doublet model (C2HDM) based on a symmetry breaking SO(6) × U (1)_x → SO(4) ×SO(2) × U (1)_x at a scale f, and explain how the effective kinetic Lagrangian of the model is obtained. The coupling of the Higgs boson as a pseudo Nambu-Goldstone boson to the standard model fields can deviate from that of the standard model Higgs boson due to the non-linear feature. These deviations cause to unitarity violation at high energies because the cancellation of the quadratic energy terms does not happen in C2HDM. We calculate the S-wave amplitude for all the possible two body to two body elastic scalar boson scatterings at the energy \sqrt{s} which involve the longitudinal component of weak gauge boson states as the corresponding Nambu-Goldstone boson states via the Equivalence Theorem Approximation. By requiring the composite two Higgs doublet model (C2HDM) to satisfy perturbative unitarity at energies reachable by the LHC, we discuss bounds on its parameters such as ξ(\upsilson^2\f^2) and the masses of extra Higgs bosons present in the scenario alongside the Standard Model (SM)-like Higgs state.