Through solving the single electron equation of motion and the FokkerPlanck equation including the terms of electric field strength and ion-acoustic turbulence, we study the influence of the ion-acoustic wave on the electron acceleration in turbulent reconnecting current sheets. It is shown that the ion-acoustic turbulence which causes plasma heating rather than particle acceleration should be considered. With typical parameter values, the acceleration time scale is around the order of 10-6 s, the accelerated electrons may have approximately a power-law distribution in the energy range 20 ～ 100 keV and the spectral index is about 3～10, which is basically consistent with the observed hard X-ray spectra in solar flares.