We report measurements of the 119Sn nuclear spin-echo decay rate 1/T2G in the heavy-fermion compound USn3. From 1/T2G, the magnetic spin-spin correlation length xi is found to vary as xi approximately T(-3/4) above approximately 100 K, which is expected for a quantum critical regime at high temperatures. Combined with the spin-lattice relaxation rate 1/T1, T1T/T2G2 is found to be temperature independent in the heavy-fermion state below T* approximately 30 K. This indicates that the heavy-fermion state of USn3 is categorized in the overdamped regime with a dynamical critical exponent z=2. These observations are consistent with a spin density wave magnetic instability at the quantum critical point.