New bifunctional cobalt catalysts for combined Fischer–Tropsch synthesis and hydroprocessing of hydrocarbons containing Pt were developed. To prepare catalysts in the form of a composite mixture, the FT synthesis catalyst Co-Al2O3/SiO2 and ZSM-5 zeolite in the H-form were used as metal and acid components, respectively, with boehmite as a binder. The catalysts were characterized by various methods, such as XRD using synchrotron radiation, SEM, EDS, TEM and TPR. The effect of the Pt introduction method on the particle size and conditions for cobalt reduction was studied. The testing of catalysts in Fischer–Tropsch synthesis was carried out at a pressure of 2.0 MPa, a temperature of 240 and 250 °C, an H2/CO ratio of 2 and a synthesis gas volumetric velocity of 1000 h−1. It is shown that the method of introducing a hydrogenating metal by adjusting the nano-sized spatial structure of the catalyst determined the activity in the synthesis and group and fractional composition of the resulting products. It is established that the presence of Pt intensified the processes of synthesis and hydrogenation, including isomeric products, and reduced the content of unsaturated hydrocarbons. The application of Pt by impregnation onto the surface of the metal component of the catalysts provided the highest productivity for C5+ hydrocarbons, and for the acidic component, it enabled maximum cracking and isomerizing abilities.