Heating with less energy consumption and environmental impacts is a major challenge confronting the world. Solid-state heat-pumping using phase-transitional materials offer a promising green solution, but these materials′ coefficient of performance (COPmat) is only about 4 ~ 23, imposing an intrinsic restriction on the energy efficiency of developed devices. Here, we propose ultrahigh-efficiency heat-pumping via the reversible heat produced by anhysteretic linear elastic deformation of martensitic alloys. We discover that many of these alloys exhibit a large adiabatic temperature change (∆T_ad) when stressed along the crystallographic directions of intrinsic giant linear thermal expansion. Material-level heat-pumping through such thermoelastic effect is demonstrated using preferentially [100]-oriented Ti78Nb22 martensitic polycrystals, achieving a giant COPmat of 87 and a cyclically stable ∆T_ad of 5 K at 473 K. Our work opens a non-phase-transitional route towards energy-efficient solid-state heat-pumping.