  We study superfluid to Anderson insulator transition of strongly repulsive
Bose gas in a one dimensional incommensurate optical lattice. In the hard core
limit, the Bose-Fermi mapping allows us to deal with the system exactly by
using the exact numerical method. Based on the Aubry-Andr\'{e} model, we
exploit the phase transition of the hard core boson system from superfluid
phase with all the single particle states being extended to the Bose glass
phase with all the single particle states being Anderson localized as the
strength of the incommensurate potential increasing relative to the amplitude
of hopping. We evaluate the superfluid fraction, the one particle density
matrices, momentum distributions, the natural orbitals and their occupations.
All of these quantities show that there exists a phase transition from
superfluid to insulator in the system.
