Josephson junctions that have ferromagnetic materials are actively studying and can be used as cryogenic memory devices. First we need to know how ferromagnetic and superconductors compete in one system. In conventional strong ferromagnets (Fe,Co,Ni) the ferromagnetic exchange energy is much larger than the superconducting gap. Therefore, it was suggested that diluted weak ferromagnetic alloys are most suitable for fabrication of superconductor/ ferromagnet/superconductor (SFS) Josephson junctions with significant Josephson critical current density. However, alloys are often characterized by a short mean-free path of electrons, which reduces the critical current. Here we study experimentally SFS junctions with a pure strong ferromagnet Ni between Nb layers. The aim is to investigate if the strong F-barrier is suitable for making SFS junction with significant Josephson coupling. We fabricate and study nano-scale Nb/Ni/Nb junctions with sizes down to 120 nm and with different thickness of Ni-barrier (2-20 nm), using 3D-FIB nanosculpturing technique. Junctions exhibit a significant critical current and Fraunhofer-like modulation Ic(H) in the in-plane magnetic field, indicating good uniformity of the junctions. We demonstrate, that Ic(H) patterns contain information about magnetization of a ferromagnetic nanoparticle, forming a junction barrier. By measuring Ic(H) patterns in different field ranges we can extract small hysteresis loops of Ni nanoparticles. We observe that Nb/Ni/Nb junctions with Ni thickness less than 4 nm have irregular Ic(H) patterns, indicating presence of micro-shots and discontinuity of the barrier. However, at larger thickness and up to ~20 nm of Ni junctions exhibit clean Fraunhofer-type modulation with significant critical current density, comparable to that of diluted F-layers with the same thickness. We argue that the observed large critical current density is due to cleanliness of pure Ni layer with a mean-free path larger than the layer thickness. Our observations suggests that it is possible to build and control Josephson devices based on strong ferromagnets, like Ni.