Based on the Boltzmann model equation, the Gas-Kinetic Unified Algorithm (GKUA) will be developed to simulate the two-dimensional micro-scale gas flows with irregular configuration. The numerical scheme for the direct evaluation of the unified velocity distribution function in the computable model of the Boltzmann equation and the multi-block grid docking technology are constructed, and the numerical procedures of characteristic-based boundary conditions are presented to model the gas-surface interaction and the inlet/outlet boundaries for the two-dimensional micro-channel flows. The two-dimensional Couette flow, the pressure-driven micro-channel flows, and the irregular micro-orifice flows in different scales are numerically solved from high rarefied free-molecule to near-continuum flow with the Knudsen numbers of $Kn$ = 100−0.01. The computed results are compared and validated with the DSMC data in the transitional flow regime and the slip N-S solutions in the near-continuum flow regime, in which the GKUA is verified accurately and smoothly to simulate the two-dimensional micro-channel flows with strong adaptability and good precision. The micro-channel flow features with the wide range of $Kn$ numbers in the near-continuum slip and transitional flow regimes are revealed, and it is probable to provide a way in developing a new numerical algorithm for micro-scale flows.