We report results about an optimized three-dimensional nanoSQUID based on niobium tunnel nanojunctions having the loop suspended to reduce the parasitic capacitance. The SQUID loop has a size of 400 x 600 nm(2) while the dimension of the square tunnel nanojunctions is 150 x 150 nm(2) with a density of the critical current of about 35 x 103 A/cm(2). The nanodevice has been characterized at liquid helium temperature; it has shown nonhysteretic current-voltage characteristics and smooth voltage-magnetic 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 300n Phi(0)/Hz(1/2) corresponding to a spin sensitivity of few Bohr magnetons for bandwidth unit.