In order to reduce the time delay of the liquid-crystal (LC) adaptive optics system (AOS) which reduces the image resolution of the observed objects, we present a new technique for the first time which is called recursive least square (RLS) modal prediction of turbulent wavefront. First, we introduce the structure of the open-loop LC AOS with RLS predictor. Second, we present the RLS modal prediction algorithm in detail. Third, an actual open-loop LC AOS is designed and built, and the RLS prediction is carried out on it. It is shown that under a pure time delay system and the turbulent condition with Greenwood frequency of 35Hz and Fried parameter of 6 cm, after prediction the residual wavefront error reduce to 0.15 wave (wave=785 nm) from 0.26 wave that is obtained through the direct open loop correction. The prediction gain reaches 42%. Finally, the images obtained by the open-loop AOS with and without prediction are demonstrated. With direct correction without prediction, the image resolution reache 25.4 cycles/mm. After the correction with RLS prediction, the image resolution reaches 32.0 cycles/mm which is equal to 0.9 of the diffraction limit resolution of the system. Therefore, with respect to correction without prediction, a relative gain of 26% in image resolution is achieved with RLS prediction. In conclusion, the RLS modal prediction can improve the image resolution of the open-loop LC AOS effectively.