We have examined the electric field observations made by the Geotail spacecraft in the near-Earth magnetotail during magnetic storms to study enhanced convection and the associated electric field that is thought to be key to causing the injection of particles into the ring current. Several recent modeling studies of the storm-time ring current suggest that an enhanced convection electric field in the magnetosphere, which is induced by a continuous southward interplanetary magnetic field (IMF), is responsible for steady particle transport into the inner magnetosphere during the storm main phase. The enhanced convection is envisioned to weaken, or cease after the main phase in response to the decrease of southward IMF, leading to the formation of a relatively symmetric ring current around the Earth during the recovery phase. However, surprisingly, our present study has not found clear evidence for the existence of such a large, steady earthward convection during either the storm main phase or the recovery phase. The observed electric field properties in the near-Earth plasma sheet are basically classified into two categories: One is characterized by intermittent bursts of fluctuating duskward electric fields associated with substorm expansions, and the other is dominated by a relatively steady, weak duskward electric field. The weak strength of the convection electric field in the latter category is seen even during storm main phase. The statistical study on this relatively steady, weak field shows that it has a weak duskward component of ~0.3 mV/m on average during both the main and recovery phases, which is almost comparable to that observed during quiet times. Their comparison with the solar wind parameters and the polar cap potential drop calculated using the Boyle model and Weimer model reveals that the weak duskward electric field tends to show poor correlation with these parameters, suggesting that storm-time convection electric field in the plasma sheet is not directly driven by either of them. These results imply that in the near-Earth plasma sheet beyond geosynchronous distance, particle injection for the storm-time ring current is not governed by enhanced convection induced by the solar wind, contrary to conclusions based on simulation studies of the storm-time ring current. The present study suggests the importance of re-examining the contribution to the ring current from the near-Earth plasma sheet for both substorm and nonsubstorm time intervals on the basis of observations made in the magnetosphere.