The effect of solar wind pressure enhancements on storm time ring current asymmetry is investigated by examining the asymmetric variations in the north-south (H) and east-west (D) components of the geomagnetic field during four magnetic storms. For two strong storms, on 25 September 1998 and 29 May 2003, pressure enhancements occurred during the main phase with strong and steadily southward IMF Bz. It is found that the pressure enhancements significantly increase the asymmetry of the already strong and asymmetric ring current under these conditions. For the moderate magnetic storm on 10 January 1997, a pressure enhancement occurred during the early recovery phase when IMF Bz was turning northward while it was still southward. Our result shows that the pressure enhancement also slightly enhanced the asymmetry of the slightly asymmetric ring current that existed during the early recovery phase. On 6 November 2000, a pressure enhancement occurred during the late recovery phase when the IMF Bz was strongly northward. For this case, the pressure enhancement did not increase the asymmetry of the already symmetric ring current. The above results of ring current asymmetry increases can be explained by considering the local energization of the preexisting ring current particles by the azimuthal electric field induced by the pressure enhancement. Our results show that the effect of pressure enhancements on the ring current depends strongly on the asymmetry state of the ring current at the times of the onsets of pressure enhancements, which is in turn determined by the IMF Bz preconditioning. In addition, the size and relative strength of a pressure enhancement also play important roles in affecting the ground asymmetric H perturbation.