The ensemble-average settling velocity, Vs, of heavy tungsten and glass particles with different mean diameters in an aqueous near-isotropic turbulence that was generated by a pair of vertically oscillated grids in a water tank was measured using both particle tracking and particle image velocimetries. Emphasis is placed on the effect of the Stokes number, St, a time ratio of particle response to the Kolmogorov scale of turbulence, to the particle settling rate defined as (Vs - V1)/ Vt where Vt is the particle terminal velocity in still fluid. It is found that even when the particle Reynolds number Rep is as large as 25 at which Vt/vk ≈ 10 where vk is the Kolmogorov velocity scale of turbulence, the mean settling rate is positive and reaches its maximum of about 7% when St is approaching to unity, indicating a good trend of DNS results by Wang and Maxey (1993) and Yang and Lei (1998). This phenomenon becomes more and more pronounced as values of Vt/vk decrease, for which DNS results reveal that the settling rate at Vt/vk = 1 and Rep<1 can be as large as 50% when St ≈ 1. However, the present result differs drastically with Monte Carlo simulations for heavy particles subjected to nonlinear drag (Rep> 1) in turbulence in which the settling rate was negative and decreases with increasing St. Using the wavelet analysis, the fluid integral time (T1), the Taylor microscale (Tλ), and two heavy particles' characteristic times (Tc1, Tc2) are identified for the first time. For St<1, Tc1 < T1 and Tc2< Tλ, whereas Tc1 ∼ T1 and Tc2= ≈ Tλ for St ≈ 1. This may explain why the settling rate is a maximum near St ≈ 1, because the particle motion is in phase with the fluid turbulent motion only when St ≈ 1 where the relative slip velocities are smallest. These results may be relevant to sediment grains in rivers and aerosol particles in the atmosphere.