  In this work, we study the three-dimensional non-Abelian noncommutative
supersymmetric Chern-Simons model with the U(N) gauge group. Using a superfield
formulation, we prove that, for the pure gauge theory, the Green functions are
one-loop finite in any gauge, if the gauge superpotential belongs to the
fundamental representation of $u(N)$; this result also holds when matter in the
fundamental representation is included. However, the cancellation of both
ultraviolet and ultraviolet/infrared infrared divergences only happens in a
special gauge if the coupling of the matter is in the adjoint representation.
We also look into the finite one-loop quantum corrections to the effective
action: in the pure gauge sector the Maxwell together with its corresponding
gauge fixing action are generated; in the matter sector, the Chern-Simons term
is generated, inducing a shift in the classical Chern-Simons coefficient.
