Conflict in the workplace affects more than just the people involved; it can create a tense working environment which can in turn affect the level of efficiency in the office. This situation becomes even more difficult when the people in question happen to be an employee and his supervisor. Resolving conflict between an employee and a supervisor generally requires the intervention of a human resources representative or another supervisor who can help to mediate the situation.
Schedule a meeting with your supervisor and address the problem directly. Explain that you know there is tension between the two of you and ask about ways to resolve it. In many instances, the issue comes down to one of communication between the two of you. Explain your side and ask him to explain his. Then, ask if there is a way to amicably resolve the situation.
Create your own solution to the problem. If either you or your supervisor--or both of you--still cannot discuss the conflict rationally, take steps to resolve it on your own. If it involves a work-related project, then resolve the issue and show your boss via your actions that you are attempting to remedy the problem. If it is an issue of personality, limit contact with your supervisor when possible and remain professional, calm and neutral during required interactions. In time, you may find the situation resolves itself simply through space between the two of you.
Refuse to make the problem worse by engaging in office politics or spreading rumors regarding the conflict. The more you antagonize your supervisor, the worse the situation may get. Refrain from commenting on the issue at all and don't spread negative rumors about your supervisor or say bad things about her. You may find yourself in a far worse situation if you do.
Request mediation from your human resources representative. Part of the job of this department is to resolve issues among employees. They can schedule a meeting with a department staff member, you and your supervisor to mediate the issue. This route is particularly beneficial because if your supervisor is treating you unfairly or is holding on to the issue despite your best efforts, it will be duly noted in this particular meeting.