New accelerator complex is being constructed by Joint Institute for Nuclear Research (Dubna, Russia) in frame of Nuclotron-based Ion Collider fAcility (NICA) project. The NICA layout includes new Booster and existing Nuclotron synchrotrons as parts of the heavy ion injection chain of the NICA Collider as well as beam transport lines which are the important link for the whole accelerator facility. Designs and current status of beam transfer systems in the beginning part of the NICA complex, which are partially commissioned, are presented in this paper.