A new method is developed for prediction of UT1. The method is based on construction of a general polyharmonic model of the Earth rotation parameters variations using all the data available for the last 80-100 years, and modified autoregression technique. A rigorous comparison of UT1 predictions computed at SNIIM with the prediction computed by IERS (USNO) in 2008-2009 has shown that proposed method provides better accuracy both for ultra-short and long term predictions.