In the construction of mountain highway, in order to avoid complicated geology and adapt to the requirements of the terrain of the large height difference and the large slope, the double-line spiral tunnels are gradually applied. The purpose of this paper is to analyze the mechanical behavior of the double-line spiral tunnel and its surrounding rock under different line curvatures, and to obtain the influence of the curvature of the spiral tunnel on the stability of the double-line tunnel construction. The analysis of this paper is based on the engineering background of double-line spiral tunnels in China’s Yunnan province. The elastoplastic three-dimensional rock strata-tunnel by means of finite difference FLAC3D software was established to simulate the construction process. The model was verified by comparing the calculation results and the actual monitoring data of tunnel vault settlement. The small curvature radius spiral makes the mechanical behavior of the double-line tunnel uneven and the surrounding rock deformed unevenly. A quantitative analysis and qualitative evaluation of the influence of curvature radius were established by the systematic evaluation index of (1) ratio of compressive stress on both sides of the tunnel, (2) stress ratio of double-line tunnel, (3) convergent deformation of the cross section of the tunnel, and (4) deformation of the surrounding rock on the top of the tunnel. The results show that the small curvature radius (less than 200 m) will make the inner pressure of the inner tunnel significantly greater than the external pressure stress, showing obvious asymmetry, and the inner tunnel vault tensile stress is greater than the outer tunnel. With the increase of the curvature radius (about more than 400 m), the ratio of the compressive stress on the inside and outside of the tunnel tends to be constant, and the bias condition is weakened and stabilized. Meanwhile, the smaller curvature radius makes the convergent deformation of the cross section of the tunnel appear asymmetrical, and the compression quantity inside the tunnel center line is larger. It provides a reference basis for the stability control of the construction of the double-line spiral tunnels in the mountainous area.