Abstract: The noncommutative space effect is a physical one in string scale. In this paper，the non-commutative ( NC) is introduced，which contains non-commutative of coordinate-coordinate，and the Moyal-Weyl product in noncommutative space can be replaced by a Bopp's shift. Then，the energy splitting of the damped harmonic oscillator in two-dimensional in non-commutative spaces are discussed.

Key words: damped harmonic oscillator in two-dimensional, noncommutative space ( NCS) , energy