The GBAR (Gravitational Behaviour of Antihydrogen at Rest) experiment at CERN has been proposed to measure the gravitational acceleration of the ultracold antihydrogen atoms. This experiment produces antihydrogen ions through interactions between antiprotons and positronium atoms. Then, antihydrogen atoms are produced for the free-fall experiment after the photo-detachment of an excess positron from the cold antihydrogen ions. The energy of the antiproton beam before the positronium target chamber will be in the range of 1-10 keV. The cross-section for the reaction between the antiprotons and positroniums depends mainly on the energy of the antiprotons. Hence, to maximize the productivity of antihydrogen ions, a sufficient number of antiprotons should be provided with well-controlled energy. In this regard, an antiproton trap is considered to accumulate and slow down antiproton beams, and cool them utilizing the electron cooling technique. This trap is designed based on the Penning-Malmberg trap, which consists of a superconducting solenoid magnet and a series of ring electrodes including high-voltage electrodes to trap antiprotons. In addition, a set of extraction electrodes and optics for beam transport are used. Each electrode has been designed and optimized using the WARP PIC simulations. In this study, the design and simulation results of each trap component are presented.