The article deals with general analysis of the modern state of ensuring rights of Ukrainian citizens by law enforcement authorities in the sphere of firearms turnover and questions of establishment, perspectives of development The Firearms Act of Ukraine. There are deep social, economic and political transformations in Ukraine nowadays. It is necessary to declare, that progressive processes of construction of the legal democratic state, except the positive ones, have unavoidable adverse effects. So, the number of persons and refugees who have no means of subsistence and constant residences has increased. Accordingly number of crimes has increased, the activity of law enforcement structures have become lower, and they have no means to provide complete protection for private, municipal, state ownership, the rights of the person, as the freedom, honor and dignity of an individual from illegal acts.