To correct horizontal turbulences, a nematic liquid crystal wavefront corrector (NLC WFC) with a fast response is used. It can linearly modulate 2pi radian at a wavelength of 633 nm. The closed-loop frequency of the adaptive optics system was originally only 12 Hz. Hence, a control system using the NLC WFC was developed, graphic processing units (GPUs) were used to compute the compensated wavefront, and the driving software for the NLC WFC was optimized. With these improvements, the closed loop frequency increased up to 60 Hz. Finally, the correction of a 500-m horizontal turbulence was performed with this fast adaptive system. After the correction, the averaged peak-to-valley (PV) and root-mean-square (RMS) values of the wavefront were reduced to 0.2 lambda and 0.06 lambda, respectively. The core of a fiber bundle is also resolved with a field angle of 0.68". As the limit of the angular resolution of the telescope is 0.65", the quasi-diffraction limited image is acquired with the closed-loop correction. It is shown that the NLC WFC has the ability to correct weak turbulences.