The infinite-layer (Sr_1-xPr_x)CuO₂ superconductor has been synthesized under high pressure. It is found that the preparation conditions, especially the calcination temperature of the starting materials and the annealing temperature under high pressure, play a key role for obtaining superconducting samples. The composition range in which superconductivity occurs in the (Sr_1-xPr_x)CuO₂ samples is =0.13-0.16. In this composition range, the sample with x=0.14 shows the maximum transition temperature of T_c(onset)=46 K and the normal-state resistivity of the samples tends to change from semiconductor-like behaviour to metal-like behaviour with increasing Pr³⁺ doping content. The microstructure of the infinite-layer (Sr_1-xPr_x)CuO₂ samples has been characterized by SEM and TEM. From electron diffraction analysis, as well as EDAX composition analysis, it has been found that in addition to the main infinite-layer phase, at least two impurity phases are present in the samples. One is an Sr-rich impurity phase having a monoclinic structure with a=4.8 AA and c=4.8 AA. Antiphase domains have been observed in this phase. The other impurity has has an orthorhombic structure with a=6.6 AA, b=5.7 AA and c=4.7 AA.