Many young people have suffered from cervical spondylosis in recent years due to long-term desk work or unhealthy lifestyles. Early diagnosis is crucial for curing cervical spondylosis. The Cobb angle method is the most common method for assessing spinal curvature. However, manually measuring the Cobb angle is time-consuming and heavily dependent on personal experience. In this paper, we propose a fully automatic system for measuring cervical spinal curvature on X-rays using the Cobb angle method, which can reduce the workload of clinicians and provide a reliable basis for surgery. Hybrid transformer network (HTN) blends a self-attention mechanism, self-supervision learning, and feature fusion. In addition, a new cervical spondylosis dataset is proposed to evaluate our method. Our model can achieve a SMAPE of 11.06% and a significant Pearson correlation coefficient of 0.9619 (p < 0.001) on our dataset. The absolute difference between the ground truth and the prediction obtained is less than 2°, implying clinical value. Statistical analysis proves the reliability of our method for Cobb angle estimation. To further prove the validity of our method, the HTN was also trained and evaluated on the public AASCE MICCAI 2019 challenge dataset. The experimental results show that our method can achieve comparable performance to state-of-the-art methods, which means that our method can measure the curvature of the neck and the entire spine.