We propose a new rate control method for JPEG image compression. Similarly to the vast majority of JPEG rate control approaches, our method solves the task of JPEG rate control by generating custom JPEG quantization tables (QTs). The method includes adaptive bit count predictor training stage, optionally followed by rate-distortion optimization (RDO) stage. The training of the adaptive bit count predictor is based on a linear prediction model using either coefficient-wise average entropy or ρ-parameter. The trained predictor is subsequently used by the RDO stage to estimate JPEG bit count resulting from the application of particular QT, thereby substantially speeding up the RDO algorithm. For RDO stage we use one of the two algorithms: Wu-Gersho algorithm or RD-OPT algorithm. The resulting hybrid design combines strong points of each of the utilized approaches, while mitigating its shortcomings, thereby providing a good trade-off between computational complexity, rate control accuracy and reconstructed image quality.