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In this thesis, the total fusion cross section sF, the fusion barrier distribution DF and the fusion probability PF, for the reactions 40Ca+44Ca, 40Ar+110Pd, 40Ca+194Pt, 46Ti+46Ti, 48Ti+60Ni, 48Ca+238U, 58Ni+54Fe, 58Ni+58Ni, 81Br+104Ru, 86kr+76Ge, 86kr+100Mo, 124Sn+96Zr, 132Sn+48Ca and 134Te+40Ca has been studied. The semiclassical approach employed in the present study is based on the theory of Alder andWinther (AW) which was originally proposed to treat the Coulomb excitation of nuclei which is called Continuum-Discretized Coupled Channels (CDCC) method. The semiclassical approach uses the Wentzel, Kramers and Brillouin (WKB) approximation to treat the classical fusion probability, whereas that the intrinsic motion is handled as a time-dependent Quantum Mechanics. To sustain our semiclassical calculations and to test its success or shortfall, we had performed full quantum mechanical calculations using the well-known CCFULL code which is used to study the fusion reactions for heavy ions. The calculations for both semiclassical and full quantum mechanical have been performed in the case of no-coupling and in the case of coupling effect included.