We investigate the ionospheric response to the 21 June 2020 annular solar eclipse using the multiinstrument observations including ionosondes, Global Navigation Satellite System (GNNS) receivers, COSMIC2, and DMSP and SWARM satellites. During the course of the eclipse, total electron content (TEC) decreased slightly in the morning at 20-70°E and largely in the afternoon at 80-150°E. However, maximum TEC depletion did not occur at the maximum obscuration, but stayed close to the southern edge of the running totality during the eclipse and near the northern edge of the elapsed totality after the eclipse. NmF2 showed the similar variation as TEC around 110°E. Meanwhile, a northward disturbance field-aligned plasma drift was observed in the eclipse region and the disturbance became strong in the southern side of the totality around 120°E. The TEC and Swarm data revealed that the crests of the equatorial ionization anomaly (EIA) enhanced on both sides of the equator around noon in~50-100°E although the northern crest was still in the Moon's shadow. The COSMIC2 profiles displayed the enhanced electron density in~300-500 km altitudes and decreased density below~300 km altitudes around the EIA crests in~70°E. The Swarm observations recorded a drop in the electron temperature both in eclipse region and in conjugate hemisphere in 77°E and 96°E. The combined effect from the electric field, neutral wind, thermal conduction, and interhemispheric photoelectron transport might result in the complicated space and time variations of ionospheric responses to the eclipse.