The kinetics of the oxidation of para-tert-butylcumene to hydroperoxide by molecular oxygen in the presence of N-hydroxyphthalimide was studied. By analyzing the laws of the formation of hydroperoxide and byproducts, a mathematical model of the process was constructed, which adequately describes the changes in the concentrations of the main components of the reaction over time. The main role of N-hydroxyphthalimide is to convert peroxide radicals into the corresponding hydroperoxides, thereby reducing the yield of byproducts by decreasing the quadratic chain termination rate. Moreover, the formed N-hydroxyphthalimide radicals increase the rate of hydrocarbon oxidation. Thus, the use of N-hydroxyphthalimide in hydrocarbon oxidation processes results in an increase in the rate and selectivity of hydroperoxide formation.