Corona virus disease 2019 (COVID-19) is an acute respiratory infectious disease with strong contagiousness, strong variability, and long incubation period. The probability of misdiagnosis and missed diagnosis can be significantly decreased with the use of automatic segmentation of COVID-19 lesions based on computed tomography images, which helps doctors in rapid diagnosis and precise treatment. This paper introduced the level set generalized Dice loss function (LGDL) in conjunction with the level set segmentation method based on COVID-19 lesion segmentation network and proposed a dual-path COVID-19 lesion segmentation network (Dual-SAUNet++) to address the pain points such as the complex symptoms of COVID-19 and the blurred boundaries that are challenging to segment. LGDL is an adaptive weight joint loss obtained by combining the generalized Dice loss of the mask path and the mean square error of the level set path. On the test set, the model achieved Dice similarity coefficient of (87.81 ± 10.86)%, intersection over union of (79.20 ± 14.58)%, sensitivity of (94.18 ± 13.56)%, specificity of (99.83 ± 0.43)% and Hausdorff distance of 18.29 ± 31.48 mm. Studies indicated that Dual-SAUNet++ has a great anti-noise capability and it can segment multi-scale lesions while simultaneously focusing on their area and border information. The method proposed in this paper assists doctors in judging the severity of COVID-19 infection by accurately segmenting the lesion, and provides a reliable basis for subsequent clinical treatment.