Chelsea have banned a fan for life for using "racially abusive language" towards Manchester City's Raheem Sterling during a match at Stamford Bridge on 8 December 2018.
Five other Blues supporters have been temporarily suspended for using "abusive language and threatening and aggressive behaviour".
Police investigated allegations England forward Sterling was racially abused but the Crown Prosecution Service said there was insufficient evidence for a criminal charge.
Chelsea conducted their own investigation and said they delayed reaching their decision so as not to prejudice the related police inquiry.
The Blues said they operated under the civil standard of proof, rather than criminal.
"While the club respects the decision of the CPS, the question it had to determine was not whether a criminal offence had been committed, but rather whether the individual acted in breach of the ticketing terms and conditions," said a Chelsea statement.
Chelsea said they sought representations from the fans concerned, reviewed video evidence, interviewed potential witnesses and took advice from two lip-reading experts.
The club statement added: "All individuals sanctioned as a result of our investigation were then offered the right to appeal and, where applicable, those appeals have been heard."
Chelsea said the six fans "crossed the line of what is acceptable".
In terms of the supporter banned for life, Chelsea said two lip-reading experts advised that racially abusive words had been used.
The other five fans have been given bans of between one and two years.
"Individuals receiving the shorter exclusion did so on the basis that they have provided undertakings about their future behaviour," said the club.
"Chelsea finds all forms of discriminatory behaviour abhorrent and we will continue to operate a zero-tolerance approach to any incidents of racism."