In this article, the magnetic and thermodynamic properties of strongly frustrated antiferromagnet are discussed. The macroscopic degeneracy caused by magnetic frustration plays a significant role on the formation of exotic ground state of frustrated antiferromagnet. Particularly, the emergence of a quantum spin liquid state has been expected on the ground state of quantum kagome antiferromagnet owing to the strong frustration and quantum fluctuation. Here, we present the unusual magnetic properties of Kapellasite type quantum kagome antiferromagnet CaCu₃(OH)₆Cl₂・0.6H₂O (Ca-Kapellasite). Magnetic properties of Kapellasite type kagome antiferromagnet depends on a balance of magnetic interactions among the nearest-neighbor J₁, the next nearest-neighbor J₂, and the further interaction Jd across the hexagon within the kagome network, and a formation of unusual magnetic state is expected including the spin liquid state. We observed the magnetic transition at 7.2 K and demonstrated that the low temperature heat capacity of Ca-Kapellasite was reproduced by assuming a two-dimensional spin-wave component and a T-linear term. The observed T-linear term of this insulating compound suggests the existence of an unusual quasi-particle excitation below the magnetic transition. This fact apparently reveal the unconventionality of the ground state of this S = 1/2 kagome antiferromagnet.