Unfortunately, no.
According to IRS rules, you may not deduct any fines you have to pay for moving violations or other civil infractions such as parking fines or tickets for failure to property maintain the vehicle. You may deduct legal fees and court costs associated with defending yourself in court as a business expense. If your license is suspended and you have to reinstate it, you may not deduct the fees associated with that process. The IRS allows you only to deduct expenses that are necessary for your income-producing activity, and speeding tickets do not qualify.
