Abstract： We study the effect of a single impurity in a one dimensional system with incommensurate lattice potential. The energy level and the wavefunction of the impurity State is derived with the Green's function technique. The energy level is found to be very sensitive to the impurity position in the region where the incommensurate potential is varying rapidly. The wavefunction of the impurity state decays exponentially with small oscillation of the amplitude. We also consider the effect of the impurity on the states in the band. For a system that is symmetric about the impurity, we find a large reduction of the amplitude of the wavefunction with even parity in the vicinity. For a system that is asymmetric about the impurity, a step-wise increase in the amplitude occurs at the impurity.