Jet pumps have been used in a lot of engineering fields. However, since the efficiency is generally low, it has been needed to improve the performance. We have numerically studied an annular jet pump without inlet swirl, and confirmed that a Reynolds stress model can reasonably predict the flow field, and the inlet swirl has the possibility to control the performance. In the present study, annular jet pumps with inlet swirl are calculated with a standard Reynolds stress turbulence model, to clarify the effects of inlet swirl of the driving jet on the mean flow field and the performance. It is shown that the inlet swirl does not change the mean flow fields remarkably, but suitable inlet swirl can contribute to the improvement of the efficiency. Moreover, it is indicated that the standard Reynolds stress model is insensitive to the change of inlet swirl.