This work reports a new method for fast whole-brain MRE using a 3D gradient-echo multishot variable-density spiral staircase acquisition. The proposed method enables high-resolution MRE by exploiting the inherently improved through-plane parallel imaging. The displacement-SNR is further enhanced by exploiting a motion encoding gradient of a 2 wave-period duration. Constrained reconstruction and deblurring method are used to generate high-quality spiral images. By integrating all these features, the proposed technique provides flexible trade-off among SNR, resolution, spatial blurring and scan time. In vivo experiments have demonstrated the capability of the proposed method for high-SNR high-resolution MRE in less than 5 minutes.