Micro-channels are prevalent extensively in microelectronic devices and heat-exchange equipment. In this study, a single-component multiphase (SCMP) pseudo-potential lattice Boltzmann model is employed to investigate the dripping of a droplet driven by gravity into micro-channels in two-dimensional coordinates. The model has capabilities that make it applicable to cases with high density ratios, low viscosities, and tunable surface tension. Tests on static droplets verify these capabilities and exhibit the effect of different parameters. Four typical deformation processes are identified: free falling, attachment, flowing, and dripping. Furthermore, the effects of different parameters, such as wettability of walls, are compared. And the critical values of dimensionless numbers are investigated. The results quantificationally shows that the critical break-up number (Ca) is increasing and the critical dripping number (Bo) is decreasing with the increase of fluid-solid strength on walls. (C) 2018 Elsevier Ltd. All rights reserved.