The project for a new injector linac for the Nuclotron–NICA accelerator tandem has been under development since 2015. The linac will accelerate protons and light ions to energies of 25 MeV and ∼7.5 MeV/nucleon, respectively. To fulfill the project, technology for fabricating superconducting RF cavities needs to be developed. The current status of the project, including the linac design, the required parameters of RF cavities, and our simulations of beam dynamics, is presented. Technological restrictions on the RF cavity parameters are discussed.