A mixed-precision program is a floating-point program that utilizes different precisions for different operations, providing the opportunity of balancing the trade-off between accuracy and performance. Precision tuning aims to find a mixed-precision version of a program that improves its performance while maintaining a given accuracy. Unfortunately, existing precision tuning approaches are either limited to small-scale programs, or suffer from efficiency issues. In this paper, we propose FPLearner, a novel approach that addresses these limitations. Our insight is to leverage a Machine Learning based technique, Graph Neural Networks, to learn the representation of mixed-precision programs to predict their performance and accuracy. Such prediction models can then be used to accelerate the process of dynamic precision tuning by reducing the number of program runs. We create a dataset of mixed-precision programs from five diverse HPC applications for training our models, which achieve 96.34% F1 score in performance prediction and 97.03% F1 score in accuracy prediction. FPLearner improves the time efficiency of two dynamic precision tuners, Precimonious and HiFPTuner, by an average of 25.54% and up to 61.07% while achieving precision tuning results of comparable or better quality.