One the most difficult things that managers, supervisors and bosses must deal with are negative employees. Sometimes poor attitudes result in a substandard work ethic or friction with other workers. But the most personally devastating employee is one who bad-mouths you. This can tarnish your reputation with subordinates and superiors, and even compromise your position with the company. The employee in question must be dealt with promptly and efficiently in order to avoid further damage. An important consideration to keep in mind is whether the employee bad-mouths everyone, or if it's just you. If the worker seems to have a vendetta against you in particular, take action to nip it in the bud.
Take the employee aside -- do not attempt to address the issue in public. Explain what you have heard from others (you can choose to mention their names or not) regarding the employee's comments about you.
Ask your employee to give his or her side of the story. Listen patiently, and do not interrupt as the worker relates this information. Determine if the bad-mouthing was the result of a miscommunication between workers, or between you and the worker.
Explain to the employee that regardless of the reason, bad-mouthing you is unacceptable and must stop. Explain why the behavior is unacceptable. (For example, it makes you look bad, lowers employee morale, and does nothing to solve possible conflicts between you.) Outline consequences if the employee does not stop the behavior, which could include write-ups and even potential firings).
Ask the employee for suggestions about how you two can have a healthier working relationship. Express that you want to get along with him or her for the sake of the company, as well as both your jobs. Make suggestions yourself as to how the relationship can improve. Outline these suggestions with the employee in writing. Set timelines and goals for carrying them out, as well as contingent plans of action if present ones fail.
Follow through with your plan.This includes completing any suggestions that you both made within the agreed upon timeframe, as well as carrying out consequences for the employee's failure to change. Carefully document all your interactions with the employee, and list any potential witnesses, in case you need to justify your actions later.