This article explores the possibilities and conditions of combustion in a pressurized water reactor of its own accumulated minor actinides (MA). The simplest computational model is used: an infinitely extended medium with the distribution and composition of all materials of the fuel assembly of the reactor core, similar to VVER-1200, with uranium dioxide having an initial 235U enrichment of 4.95%. The burnup model is presented in the form of iterations, each of which simulates a fuel campaign lasting 4 years without refueling. At the start of the cycle, special fuel rods are loaded with minor actinides extracted from the reprocessed SNF of the VVER-1200 reactor. After the end of the fuel campaign, all the MAs are removed from the SNF and used in a new iteration. As a result of calculations, it was found that the MA mass in the cycle after 3–7 iterations (depending on the number of fuel elements allocated for the placement and accumulation of MAs) tends to an equilibrium state (regardless of the MAs added every 4 years). In other words, the fuel rods allocated for loading MAs play the role of a kind of furnace, into which, in each iteration, MAs from the previous iteration accumulated in the given reactor are loaded. After several iterations, the burned MA mass converted into fission products is compared with the incoming one. The inclusion of MAs in this way into the fuel cycle converts at least 86% of MAs into fission products without affecting the power generation of the nuclear power plant. It is important that MAs are temporarily unloaded from the reactor after the next iteration in order to remove fission products and to add a new portion of MAs. After stopping the reactor operation, about 16% of the total amount of MAs generated for the entire history of the reactor’s life is discharged into the storage facility. The initial fuel composition in the fuel rods allocated for loading MAs differs from the others only in the amount of MAs and the mass of 238U. The simplified computational model used in this work (without annual overloads of the reactor) influenced the burnup depth and, naturally, the duration of operation, i.e., the k∞ value becomes less than 1 after 1056 days instead of the actual 1460 days with annual fuel overloads. This affected the average fuel composition and, consequently, the neutron spectrum, and could affect the main result of the work, i.e., the number of burned-out MAs in different iterations. Additional calculations, taking into account the annual overloads of the reactor, showed that the change in the spectral composition had little effect on the amount of MAs at the end of the fuel campaign (within 2%). It turned out that the replacement of 238U with minor actinides in fuel rods, the number of which is less than 10, leads to a loss of reactivity. When the number of fuel rods for loading MAs is more than 10, the reactivity increases, giving hope for burning up MAs accumulated in several reactors.