We found a very large , \sim 35 kpc , emission-line region around the Seyfert type 2 galaxy NGC 4388 , using deep narrow-band imaging with the prime focus camera ( Suprime-Cam ) of the Subaru telescope . This region consists of many faint gas clouds or filaments , and extends northeastwards from the galaxy . The typical H \alpha luminosity L ( H \alpha ) of the clouds is \sim 10 ^ { 37 } erg s ^ { -1 } , and the total L ( H \alpha ) of the region within 10 kpc from the nucleus is \sim 2 \times 10 ^ { 38 } erg s ^ { -1 } , which corresponds to an ionized gas mass of \sim 10 ^ { 5 } M _ { \sun } . The map of the emission-line intensity ratio I ( [ O iii ] ) / I ( H \alpha ) indicates that the inner ( r < 12 kpc ) region of the VEELR may be excited by nuclear ionizing radiation . The excitation mechanism of the outer ( r > 12 kpc ) region is unclear , but it is likely that the nuclear radiation is also a dominant source of its ionization . We discuss the origin of the ionized gas . Two plausible origins of the gas in the VEELR are ( i ) the tidal debris resulting from a past interaction with a gas-rich dwarf galaxy , i.e. , a minor merger , or ( ii ) the interstellar medium of NGC 4388 , stripped by the ram pressure of the hot intracluster medium of the Virgo cluster .