In this paper, a numerical methodology for modeling contact line motion in a dual-grid level-set method (DGLSM) - solved on a uniform grid for interface which is twice that for the flow equations - is presented. A quasi-dynamic contact angle model - based on experimental inputs - is implemented to model the dynamic wetting of a droplet, impacting on a hydrophobic or a superhydrophobic surface. High-speed visualization experiments are also presented for the impact of a water droplet on hydrophobic surfaces, with non-bouncing at smaller and bouncing at larger impact velocity. The experimental results for temporal variation of the droplet shapes, wetted-diameter and maximum height of the droplet match very well with the DGLSM based numerical results. The validation of the numerical results is also presented with already Published experimental results, for the non-bouncing on a hydrophobic and bouncing on a superhydrophobic surface, at a constant impact velocity. Finally, a qualitative as well as quantitative performance of the DGLSM as compared to the traditional level set method (LSM) is presented by considering our experimental results. The accuracy of the partially refined DGLSM is close to that of the fine-grid based LSM, at a computation cost which is close to that of the coarse-grid based LSM. The DGLSM is demonstrated as an improved LSM for the computational multi-fluid dynamics (CMFD) simulations involving contact line motion. (C) 2016 Elsevier Ltd. All rights reserved.