In this work, a numerical solution of flow and heat transfer of a micropolar fluid in a lid-driven cavity under different micro-gyration boundary conditions is presented. A finite difference method is employed to solve the governing system of partial differential equations. The cases of strong concentration of microelement and weak concentration of microelement are considered. The effects of the governing parameters, namely the dimensionless time parameter, micro-gyration boundary conditions parameter and vortex viscosity parameter on the streamlines contours and temperature contours as well as the velocity profiles at the enclosure mid-section, angular velocity profiles at the enclosure mid-section, Nusselt number and average Nusselt number at the bottom and top walls of the enclosure are investigated. The results for the Newtonian fluid condition are validated by favorable comparisons with previously published results. The numerically results are shown graphically to illustrate special features of the solutions. The values of the average Nusselt number at the bottom and top walls of the enclosure are presented in tables.