Identifying interactions between compounds and proteins is an essential task in drug discovery. To recommend compounds as new drug candidates, applying the computational approaches has a lower cost than conducting the wet-lab experiments. Machine learning-based methods, especially deep learning-based methods, have advantages in learning complex feature interactions between compounds and proteins. However, deep learning models will over-generalize and lead to the problem of predicting less relevant compound-protein pairs when the compound-protein feature interactions are high-dimensional sparse. This problem can be overcome by learning both low-order and high-order feature interactions. In this paper, we propose a novel hybrid model with Factorization Machines and Graph Neural Network called FMGNN to extract the low-order and high-order features, respectively. Then, we design a compound-protein interactions (CPIs) prediction method with pharmacophore features of compound and physicochemical properties of amino acids. The pharmacophore features can ensure that the prediction results much more fit the expectation of biological experiment and the physicochemical properties of amino acids are loaded into the embedding layer to improve the convergence speed and accuracy of protein feature learning. The experimental results on several datasets, especially on an imbalanced large-scale dataset, showed that our proposed method outperforms other existing methods for CPI prediction. The western blot experiment results on wogonin and its candidate target proteins also showed that our proposed method is effective and accurate for finding target proteins. The computer program of implementing the model FMGNN is available at https://github.com/tcygxu2021/FMGNN.