CNTs/Al-Li composite was first prepared by hot-pressed sintering from Al-Li alloy powder and CNTs solution, and then the hot compression tests were performed on MMS-100 thermal simulator at strain rate range of 0.01– 10 s− 1, deformation temperature range of 350–500 °C, and total deformation amount of 60%. True stress–strain curves were plotted, and constitutive equation as well as hot processing maps were successfully confirmed based on Arrhenius constitutive model and Prasad instability criterion. Results show that CNTs/Al-Li composite have a very poor hot deformation ability and narrow processing region, which is strain rate range of 0.1–1 s− 1 and deformation temperature range of 360–400 °C. Hot extrusion experiment was carried out and the processing parameters were selected according to the established hot processing map, and an improvement on strength and a good balance between strength and plasticity can be obtained, which is about 650 MPa for tensile strength and 9% for elongation.