Motivated by recent experimental progress on triangular lattice heavy-fermion compounds,we investigate possible Lifshitz transitions and the scanning tunnel microscope (STM) spectra of the Kondo-Heisenberg model on the triangular lattice.In the heavy Fermi liquid state,the introduced Heisenberg antiferromagnetic interaction (JH) results in the twice Lifshitz transition at the case of the nearest-neighbour electron hopping but with next-nearest-neighbour hole hopping and the case of the nearest-neighbour hole hopping but with next-nearest-neighbour electron hopping,respectively.Driven by JH,the Lifshitz transitions on triangular lattice are all continuous in contrast to the case on square lattice.Furthermore,the STM spectra shows rich line-shape which is influenced by the Kondo coupling JK,the Heisenberg antiferromagnetic interaction JH,and the ratio of the tunneling amplitude of f-electron tf versus conduction electron tc.Our work provides a possible scenario to understand the Fermi surface topology and the quantum critical point in heavy-fermion compounds.