Head pose estimation is a typical computer vision task that has been applied to many helpful applications. It is still challenging due to occlusions, low resolution, and extreme pose changes. A method is proposed for landmark-free head pose estimation in a fusion inception deep neural network. The fusion inception network is developed to predict head pose angles without landmarks in RGB images only, which avoids the error caused by landmark location faults. A three-channel prediction module in the developed network is designed to perform classification and regression jointly. A data augmentation method is proposed for sample expansion to alleviate overfitting. A balance loss strategy is proposed to take place of cross-entropy for pose angle classification. The developed balance loss can be applied to deal with class imbalance. The proposed method has excellent performance in head pose estimation by comparison with state-of-the-art methods on some challenging datasets.