We have studied the melting process of a finite-sized two-dimensional colloidal crystal by video microscopy. The local area fraction ϕ and the local hexatic orientational order parameter ψ(6) have been evaluated for respective Voronoi cells in the crystal. The histogram of ϕ exhibits a peak and the peak ϕ continuously decreases with the time elapsed. The histogram of |ψ(6)| shows an abrupt broadening for ϕ < 0.65. This critical value of ϕ is the transition point between the hexatic and dense liquid phases in finite crystal. We have also evaluated ϕ and |ψ(6)| as a function of the distance from the center of the crystal r. ϕ(r) is almost constant within the crystal and monotonously decreases with the time elapsed. |ψ(6)(r)| gradually decreases with r but there is the core with |ψ(6) = 1 at earlier time stage. The temporal change of the average ϕ within the crystal is qualitatively explained by the slow diffusion of the particles situated at the crystal edge. The steric repulsion between the particles within the crystal enhances the expansion rate of the crystal edge. Overall melting behavior is same in the crystals with different sizes. We have also studied the melting of a finite-sized crystal composed of soft-core particles by Brownian dynamics simulation and verified the finite-size effect on the melting process. The simulated behavior is qualitatively in good agreement with the experimental results.