The fight against crimes of a terrorist nature is a task of international importance. Modern penitentiary systems in various countries were not ready for effective work aimed at preventing international terrorist threat. Persons convicted of committing terrorist crimes are currently serving their sentences in non-specialized correctional institutions that do not involve targeted counter-terrorism preventive measures with convicts. On the contrary, representatives of Islamic terrorist organizations are actively using the prison environment to propagate pseudo-religious ideas that encourage terrorism. One of the few attempts to prevent Islamist terrorism among people suspected or convicted of terrorist crimes was made by the US leadership at the beginning of the XXI century. The American penitentiary experience shows that the use of purely punitive methods of correcting a criminal terrorist does not guarantee the convict’s refusal to carry out terrorist activities. Therefore, it is necessary to develop a model of a special type of penitentiary institution aimed at providing an effective prevention of terrorist activity and suppressing the recruitment of new participants to terrorist organizations. The main preventive measures to use in this type of correctional institution should be the separate maintenance of convicts representatives of various social groups, as well as educational and religious activities explaining the true social values observed both by Islam and other world religions.