  Deformation quantization is a powerful tool to quantize some classical
systems especially in noncommutative space. In this work we first show that for
a class of special Hamiltonian one can easily find relevant time evolution
functions and Wigner functions, which are intrinsic important quantities in the
deformation quantization theory. Then based on this observation we investigate
a two coupled harmonic oscillators system on the general noncommutative phase
space by requiring both spatial and momentum coordinates do not commute each
other. We derive all the Wigner functions and the corresponding energy spectra
for this system, and consider several interesting special cases, which lead to
some significant results.
