We present the first 3-D images of P-wave radial anisotropy (RAN) and azimuthal anisotropy (AAN) down to 750-km depth beneath Greenland and surrounding regions. The results are obtained by applying a regional tomographic method to simultaneously invert P wave arrival times of 1,309 local events and P wave relative traveltime residuals of 7,202 teleseismic events, which were recorded mainly by the latest GLISN network. A high-velocity body located beneath northeast Greenland (NEG) to its offshore exhibits a strong negative RAN and a strong AAN with N-S to NE-SW oriented fast-velocity directions (FVDs). The FVDs are generally consistent with the direction of the fold axis of the Caledonian fold belt, which is considered as an outcrop of the NEG body on land. Beneath the Iceland, Jan Mayen, and Svalbard hotspots, a strong positive RAN and a negligible or weak AAN are revealed, which may reflect effects of upwelling mantle plumes. Among the three regions, a weak AAN with a constant FVD is only revealed beneath Iceland, which may reflect the existence of background mantle flow. The RAN and AAN features beneath the Labrador Sea, Davis Strait, and Baffin Bay suggest the following scenario on breakup between Greenland and Canada: the breakup was initiated at the Labrador Sea due to local mantle upwelling, but the northward propagation of the breakup was blocked by a strong high-velocity anomaly beneath Davis Strait; the opening of Baffin Bay might be caused passively by far-field plate forces.