India holds the record of most consecutive innings of over 400, 6 consecutive innings
From Oct 1986 in an inning against Australia in Mumbai when India scored 517/5d, till Feb 1987, inning against Pakistan in Kolkata, when India recorded 403, India scored more than 400 runs in 6 consecutive innings. Thus, India holds the record of most consecutive innings of over 400, 6 consecutive innings.