Percolation path is a very important concept related with statistics, physics and many other subjects. In previous studies, researchers have studied the practical applications of percolation theory and the properties of percolation threshold. However, there are still many unidentified properties of percolation path that are closely related with some important practical problems. Therefore, in this study, an algorithm to simulate percolation based on Monte Carlo method is introduced. In this study, the percolation threshold is not the only focus. Instead, the variation trend of the pattern of percolation path is of primary concern. Another concept called fractal dimension is introduced to analyze this property. Based on the analysis result, it is concluded that there exist percolation thresholds for 2-D lattices and the pattern of percolation paths is closely related with its fractal dimension. Some other factors are also taken into consideration. Under different circumstances, the performance of percolation path will differ.