Ambipolar diffusion (AD) is a key process in molecular clouds (MCs). Non-ideal MHD turbulence simulations are technically very challenging because of the large Alfvén speed of ions in weakly ionized clouds. Using the Heavy-Ion Approximation method (Li, McKee & Klein 2006), we have carried out two-fluid simulations of AD in isothermal, turbulent boxes at a resolution of 5123, to investigate the effect of AD on the weakly ionized turbulence in MCs. Our simulation results show that the neutral gas component of the two-fluid system gradually transforms from an ideal MHD turbulence system to near a pure hydrodynamic turbulence system within the standard AD regime, in which the neutrals and ions are coupled over a flow time. The change of the turbulent state has a profound effect on the weakly ionized MCs.