Zíb first celebrated success on the Challenger Tour . In his career he won seven singles titles and four more doubles. He celebrated his greatest success on the ATP World Tour in Valencia in 2006 when he and David Škoch defeated Lukáš Dlouhý and Pavel Vízner in the purely Czech final . He was also in the final once again in Acapulco . In Grand Slam tournaments , he did not get past the second round in either singles or doubles.
In 2005 and 2006 Zíb was nominated three times for the Czech Davis Cup team . He lost both his singles and doubles in the first round match against Argentina in 2005 . In the subsequent relegation game against Germany he lost to Nicolas Kiefer and Tommy Haas in the singles. It wasn't until 2006 that he won his first Davis Cup victory against Morocco : He won both singles. In 2009 he played tennis tournaments regularly for the last time.