Although air transport contributes to globalization, airline emissions have attracted focus in green logistics. In this work, we investigate the airline-fleet assignment problem from a risk-averse perspective in which uncertain demand and fuel price are considered simultaneously. The objective is to maximise the total profit in a risk-averse fashion, i.e., the weighted sum of the expected profit and the conditional value at risk of profit. An appropriate assignment can reduce fuel use and carbon dioxide emissions. For the problem, a two-stage stochastic programming model is constructed. The first stage consists of assigning aircraft families to flight legs, while the second stage determines specific aircraft deployment with the realized information. To solve the problem, a sample average approximation (SAA) approach is firstly applied. An efficient string-based heuristic is, further, developed. Numerical experiments are conducted and sensitivity analysis is performed. The results show the efficiency of the proposed heuristic and managerial insights are drawn.