It has been proposed that, in the near-Earth magnetotail, earthward propagating flux ropes can merge with the Earth's dipole magnetic field and dissipate its magnetic energy. However, the reconnection diffusion region related to this process has not been identified. Here we report the first in situ observation of magnetic reconnection between an earthward propagating flux rope and the closed magnetic field lines connecting to Earth. Magnetospheric Multiscale (MMS) spacecraft crossed a vertical current sheet between the leading edge of the flux rope (negative B-Z) and the geomagnetic field (positive B-Z). The subion-scale current sheet, super-Alfvenic electron outflow, Hall magnetic and electric field, conversion of magnetic energy to plasma energy (J.E > 0), and magnetic null were observed during the crossing. All the above signatures indicate that MMS detected the reconnection diffusion region. This result is also relevant to other planets with intrinsic magnetosphere. Plain Language Summary Magnetic reconnection is an essential source process in space weather. Reconnection produces many magnetic structures, such as the magnetic flux ropes and reconnection fronts, and ejects them away from the reconnection site. These structures interact with the surrounding space environment during its propagation, which may have great geomagnetic effects. A highly asymmetric earthward propagating magnetic flux rope is often observed in the Earth's magnetotail. It has long been suggested that this asymmetrical magnetic flux rope is formed due to the flux erosion of the earthward part of the flux rope by magnetic reconnection between the flux rope and the geomagnetic field. Despite various theoretical and numerical simulation studies, there has been no observational evidence to confirm this scenario. This paper reports the first observation of magnetic reconnection occurring at the earthward front of a flux rope in the Earth's magnetotail, confirming the previous theoretical predictions and explaining the formation of the asymmetric flux rope which is often observed in the near-Earth magnetotail.