Kelvin-Helmholtz instability of two-dimensional immiscible incompressible fluid in a sloping tube was numerically simulated with front tracking method. Effects of inclined angles of wall, thickness of velocity gradient layer and Richardson number on development of K-H instability were investigated. It shows that the greater the angle of wall inclination is, the faster the K-H instability develops and the more liquid is rolled up. It was also found that increase of thickness of the velocity gradient layer under the inclined wall presented an inhibitory effect on roll-up of the interface. The greater gravity items of Richardson number is, the slower the interface rolls up. However, surface tension items of Richardson number have weak effect on the growth of interface.