Since 2009, in addition to drivers with a standard driver's license, a new category of drivers also takes part in the traffic on the roads in Serbia - those who have a trial driving license for motor vehicles of certain categories. Some of these drivers are adults, but some of them are minors. Very often, this category of drivers also participates in traffic accidents. Police officers who investigate traffic accidents involving drivers with trial driving licenses - according to the available data - rarely after these incidents lodge appropriate criminal charges against parents or guardians of minor drivers with trial driving licenses because they failed to exercise control over their children or children who are entrusted to their care. In this paper, we present the relevant criminal regulations and the possibility to initiate appropriate proceedings against the parents or guardians of minor drivers with trial driving licenses. We consider that the initiation of criminal proceedings against parents or guardians for failing to control the underage child who is a driver with trial driving license is the best solution with a view to increasing the safety of all participants in road traffic, and above all minors. We try to point out to the possibilities available to members of the police to initiate appropriate criminal proceedings not only against minors with probationary driving licenses, but also against their parents or certain categories of guardians. At the same time, we believe that after the commencement of criminal proceedings, during the court procedure, it is necessary to strictly punish persons who have neglected the duty of supervision. By virtue of the validity of such judgments it is necessary, in cooperation with the media, to indicate that not only preventive but also repressive measures are taken against parents or guardians who do not exercise control over their children. We have also given some suggestions from the aspect of court practice.