  We study an energy spectrum of electron moving under the constant magnetic
field in two dimensional noncommutative space. It take place with the gauge
invariant way. The Hofstadter butterfly diagram of the noncommutative space is
calculated in terms of the lattice model which is derived by the Bopp's shift
for space and by the Peierls substitution for external magnetic field. We also
find the fractal structure in new diagram. Although the global features of the
new diagram are similar to the diagram of the commutative space, the detail
structure is different from it.
