  We study thermal properties of one dimensional(1D) harmonic and anharmonic
lattices with mass gradient. It is found that the temperature gradient can be
built up in the 1D harmonic lattice with mass gradient due to the existence of
gradons. The heat flow is asymmetric in the anharmonic lattices with mass
gradient. Moreover, in a certain temperature region the {\it negative
differential thermal resistance} is observed. Possible applications in
constructing thermal rectifier and thermal transistor by using the graded
material are discussed.
