Former Major League Baseball relief pitcher, Arthur Rhodes, had the most consecutive scoreless games. He had a scoreless streak of 33 games while pitching in relief for the Cincinnati Reds over a 30-inning span from 13 April to 26 June 2010. Rhodes’ feat matched the Major League Baseball (MLB) record for most consecutive appearances without allowing a run, a record previously set by Mike Myers of the Colorado Rockies in 2000 and Mark Guthrie of the New York Mets in 2002.
Source: www.guinnessworldrecords.com, SPOKEO