A study on the superconducting RF linac is underway in order to increase the beam energy up to 1 GeV by extending the Proton Engineering Frontier Project (PEFP) 100-MeV linac. The operating frequency of the PEFP superconducting linac (SCL) is 700 MHz, which is determined by the fact that the frequency of the existing normal conducting linac is 350 MHz. A preliminary study on the beam dynamics showed that two types of cavities with geometrical betas of 0.50 and 0.74 could cover the entire energy range from 100 MeV to 1 GeV. An inductive output tube (IOT) based RF system is under consideration as a high-power RF source for the SCL due to its low operating voltage and high efficiency. As a prototyping activity for a reduced beta cavity, a five-cell cavity with a geometrical beta of 0.42 was designed and fabricated. A vertical test of the prototype cavity at low temperatures was performed to check the performance of the cavity. The design study and the prototyping activity for the PEFP SCL will be presented in this paper.