The correlation between plasmoids and geomagnetic substorms has been demonstrated by satellite observations. In addition to the tailward propagating plasmoids with N‐S bipolar signatures, earthward propagating plasmoids are found, which are characterized by plasma sheet S‐N bipolar events and lobe S‐N bipolar signatures. The occurrence rate of the S‐N bipolar events is much lower than that of the N‐S events. The S‐N bipolar events occur primarily during quiet geomagnetic and IMF Bz north period, and they are correlated with small, isolated geomagnetic substorms. A 2.5 dimensional MHD simulation on the earthward propagating plasmoids has been carried out, on base of the specific distribution of the cross‐tail electric fields Ey during geomagnetically quiet times (IMF Bz is northward and | By |≥ Bz). The simulation results of the two cases showed the major features of the flux rope magnetic structures and plasmoids with complex closed magnetic field lines. The similar signatures to tailward propagating plasmoids could be consistent with IMP 8 observations about the earthward propagating plasma sheet S‐N bipolar events. The results displayed a similar configuration to the schema given by Schindler which may explain the low occurrence frequency of the S‐N events, and also showed that the dynamic growth of the magnetic reconnection becomes considerably suppressed for a strong cross‐tail magnetic field By. From this simulation it could be concluded that the magnetic reconnection can be the genetic mechanism of the plasma acceleration and heating in the magnetotail in both geomagnetically active and quiet time, namely, under both southward and northward (with | By |≥ Bz) IMF conditions.