Flux-rope/TCR events near the magnetotail lunar orbit(-67R_E < GSM X* < -39RE) were studied using magnetic-field and plasma data measured by THEMIS B and C between January 2011 and March 2012. The aberrant coordinate GSM*, where the X* axis is rotated 4° relative to GSM-X, was used to count the occurrence rate. The number ratio of earthward to tailward events was about 3:5. Moreover, the event occurrence rate distribution showed a clear dawn-dusk asymmetry distribution, with dusk-side events accounting for 57.98%. A superposed epoch analysis of the flux-rope events showed that earthward events had a shorter duration in the leading than in the trailing part. Earthward events also displayed a lower temperature and a lower flow speed than tailward events. We studied the relationship between the event occurrence rate and geomagnetic activity level even further. The occurrence rate of tailward flux-rope/TCR events increases with increasing AE-index, whereas earthward events occur mainly in the relatively quiet period of geomagnetic activity(AE ~ 100–300 n T). Flux-rope/TCR events identified within a 10 mm time frame were treated as belonging to a single reconnection event. By comparing the occurrence rates of earthward and tailward events along X*, we estimated the most likely location of the near-Earth reconnection site as X* = -36R_E. Flux-rope / TCR events near the magnetotail lunar orbit (-67R_E