The microstructural evolution in a thin Cu film with nano-crystallized columnar structure is investigated with transmission electron microscopy (TEM) after being annealed at 250℃ for various times and with computer simulation method. Experimental results show that the average grain size increases linearly with annealing time. A two-dimensional 3-connected network with straight line is assumed and the line tensions acting on vertices are considered only. The simulation results show that, prior to disappearance of small grains, the distribution of angles between lines at vertices tends to 2π/3. The change in grain area for both individual grain and average ones with the same number of sides qualitatively satisfies Von Neumann's law. During the process of disappearance of small grains, the distribution of angles remains similar. However, the distribution of grain shapes (the number of sides) is not time invariant, but broadens with increasing time. The calculation indicates that the average size of grain increases linearly with time. This is consistent with experimental results and can be expected to application in estimating the variation of grain size of thin films at elevated temperature that can be encountered both in post-fabrication and service.