We recently proposed a new discharge process caused by streaming cosmic rays (CRs) in the universe. The CRs current drives a return current of thermal electrons to compensate for the CR current. Then, a resistive electric field is induced by the resistivity of the return current. In this work, we show that the resistive electric field can accelerate secondary electrons which is generated by the CRs. We investigate the evolution of the energy spectrum of secondary electrons by solving the Boltzmann equation numerically. The discharge accelerates high-energy secondary electrons, resulting in enhancements of ionization and heating. The return current of thermal electrons is not fully replaced by the electric current of secondary electrons after the discharge. In a quasi-steady state, although the resistive electric field is weaker than one before the discharge, the weak resistive electric field accelerates the secondary electrons weakly. The quasi-steady state spectrum of secondary electrons is formed by a balance of the weak acceleration and the energy loss due to excitation and ionization of hydrogen atoms or molecules.