How can I sue a game website who banned my account without any reason?

The company can ban you for violation of its Terms of Service. Most Terms of Service will give the company the right to ban your account if, in the judgment of the company, it needs to be banned. The company is allowed to protect itself and other users. In most cases, the company is not required to tell you the reason. If you think the company has you mixed up with someone else and if your legal record and your behavior are squeaky clean, and if the same is true of everyone else who may use your account, you may want to contact the company and plead your case. If it is a choice between banning your account and risking having a potential abusive user, the company will ban the suspect user.