The creation and control of homogeneous isotropic turbulence in laboratory settings is of practical significance. In this paper, we propose a novel design for a turbulence generation apparatus driven by two pairs of oscillating grids, with the object of striking a balance between the stochastics of momentum injection and the flexibility of control of turbulent kinematic energy (TKE). To validate the performance of this system, tomographic particle image velocimetry measurements are conducted. Based on Reynolds decomposition, we characterize the secondary flow pattern and examine the impact of the mean velocity on the TKE transport. Analysis of one- and two-point statistics indicates that the generated turbulence exhibits reasonable approximations of homogeneity and isotropy. The TKE and the dissipation rate are linearly proportional to the grid oscillation frequency, with the Taylor-scale Reynolds number Reλ ranging from 47 to 154, suggesting a convenient control of turbulence with low-to-moderate intensity.