Gradient-index metamaterial is crucial in the spatial manipulation of electromagnetic wave. Here we present an efficient approach to extend the bandwidth of phase modulation by utilizing the broadband characteristic of low-quality (Q) meta-surface in the reflection mode. The dispersion of the meta-surface is engineered to compensate the phase difference induced by frequency change. Meanwhile, a thin gradient index cover layer is added on the top of meta-surface to extend the phase modulation range to cover the entire [0, 360 degrees]. As a proof of concept, anomalous nearly perfect reflection with relative bandwidth near 40% is demonstrated in the microwave regime. (C) 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.