An improved method for generating nearly orthogonal grids for various 2-D shapes has been implemented with fixed, sliding and time variant boundaries for single and multiblock domains. Sliding boundaries are used for achieving orthogonality of grid lines at the boundaries, which in turn effect the interior grid point locations, and so the resulting grid lines become almost orthogonal to each other. The generating system is based on solution of a system of elliptical equations with finite difference discretization using bilinear interpolation as an initial guess. The influence of number of grid points, grid quality control quality function and grid properties are investigated.