Magnetic resonance imaging of the nanoscale resolution will be a powerful non-destructive probing tool to for the Biology and Material Science. As the imaging voxel shrinks into the nanoscale, the number of spins that can generate a resonance signal become very small. Fortunatly, the SQUID miniaturized into nanoscale is promising in the inductive detection of a single electron spin. Therefore, A nano-SQUID with a strong spin coupling coefficient, a low flux noise, and a wide working magnetic field range is highly desired in a single spin resonance measurement. The nano-SQUID with Dayem-bridge junctions are excel in a high working field range and a direct coupling from spins to the bridge. However, the common planar structure of nano-SQUID is known for problems such as a shallow flux modulation depth and a readout-troublesome hysteresis in the current-voltage curves. Here, we developed a fabrication process for a 3D Nb nano-SQUIDs with nano-bridge junctions. The characterization of the device shows a up to 45.9% modulation depth with a reversible current-voltage curve. Owning to the large modulation depth, the measured flux noise is as low as 0.34 μΦ0/Hz1/2. The working field range of the SQUID is more than 0.5 T. We believe that the 3D Nb nano-SQUIDs provides a promising step towards the single-spin inductive detection.