We report results about an optimized three dimensional nanoSQUID based on niobium tunnel nano-junctions having the loop suspended to reduce the parasitic capacitance. The SQUID loop has a size of 400x600 nm2 while the dimension of the square tunnel nano-junctions is 150x150 nm2 with a density of the critical current of about 35x103 A/cm2. The nano-device has been characterized at liquid helium temperature; it has shown nonhysteretic current-voltage characteristics and smooth voltagemagnetic flux characteristics resulting in a very stable operation in a wide range of bias points. The spectral density of the magnetic flux noise in the white region, measured with a two-stage noise measurement setup was as low as 300 nF0/Hz1/2 corresponding to a spin sensitivity of few Bohr magnetons for bandwidth unit.