The mechanism of wound closure in epithelial tissues, i.e., cell monolayer sheets, is investigated through computer simulations. A wound means an area in which some cells have been removed from the normal tissue. The vertex dynamics cell model [T. Nagai and H. Honda, Philos. Mag. B 81, 699 (2001)], which describes morphogenesis of epithelial tissues using the concepts of statistical physics, is modified and applied to the closure of small wounds without mitosis. It is shown that cell-basal-lamina adhesion governs the wound closure competing with cell-cell adhesion and cell elasticity. The simulation results reproduce the actual wound closure process qualitatively and partly quantitatively. The closing proceeds with the translation of the edges of wound polygons toward the wound center and the intermittent reduction in the number of polygon edges. Over time, the process leads to an exponential decrease in the wound area. A shape factor is introduced to describe the wound shape quantitatively and is used to examine the time variation thereof. A method for determining model parameters by comparison with the experiments is given.