  We construct a deformed Wess-Zumino model on the noncommutative superspace
where the Bosonic and Fermionic coordinates are no longer commutative with each
other. Using the background field method, we calculate the primary one-loop
effective action based on the deformed action. By comparing the two actions, we
find that the deformed Wess-Zumino model is not renormalizable. To obtain a
renormalizable model, we combine the primary one-loop effective action with the
deformed action, and then calculate the secondary one-loop effective action
based on the combined action. After repeating this process to the third time,
we finally give the one-loop renormalizable action up to the second order of
Bosonic-Fermionic noncommutative parameters by using our specific techniques of
calculation.
