The issue of carbon emissions from civil aviation has received extensive global attention because of its rapid growth rate and difficulty in reducing emissions. Incorporating civil aviation into the carbon market not only promotes technological innovation, but also accelerates the realisation of the dual-carbon goal. In this context, the allocation of carbon emission allowances to Chinese airlines is studied based on the fairness principle to provide a theoretical basis for the establishment of the Chinese civil aviation carbon market. Combining the pros and cons of the grandfather principle and the ability-to-pay principle, a multi-objective planning model is constructed, and ten more influential airlines are used as examples for allocation. The results show that Chinese airlines need to make certain emission reduction measures if they want to meet the requirements of the 14th Five-Year Development Plan of Civil Aviation.