The nickelate Pr4Ni3O8 features quasi-two-dimensional layers consisting of three stacked square-planar NiO2 planes, in a similar way to the well-known cuprate superconductors. The mixed-valent nature of Ni and its metallic properties makes it a candidate for potentially unconventional superconductivity. We have synthesized Pr4Ni3O8 by topotactic reduction of Pr4Ni3O10 in 10% hydrogen gas, and report on measurements of powder-neutron diffraction, magnetization, and muon-spin rotation (µSR). We find that Pr4Ni3O8 shows complicated spin-glass behavior with a distinct magnetic memory effect in the temperature range from 2 to 300 K and a freezing temperature Ts≈68K. Moreover, the analysis of µSR spectra indicates two magnetic processes characterized by remarkably different relaxation rates: a slowly relaxing signal, resulting from paramagnetic fluctuations of Pr/Ni ions, and a fast-relaxing signal, whose relaxation rate increases substantially below ≈70K which can be ascribed to the presence of short-range correlated regions. We conclude that the complex spin-freezing process in Pr4Ni3O8 is governed by these multiple magnetic interactions. It is possible that the complex magnetism in Pr4Ni3O8 is detrimental to the occurrence of superconductivity.