Global warming, mainly caused by human activities, demands urgent reduction of greenhouse gas emissions. Establishing a carbon market central to this effort involves the allocation of carbon emission quotas. The uncertainty of consensus cost in the carbon market will bring the risk of loss to the whole consensus process. In this paper, we focus on solving the problem of group consensus decision with risk averse decision maker. First, three new distributionally robust two-stage minimum asymmetric adjustment cost consensus models based on conditional value at risk (CVaR) are proposed. Considering that it is difficult to obtain historical decision-making data with risk in the carbon market, a novel box ambiguous set and a polyhedron ambiguous set are constructed, respectively. The risk expectation cost of group consensus decision-making problem under the worst-case condition is measured. Then, a computable linear equivalent form of the proposed model is derived in order to facilitate calculation. Finally, numerical cases based on carbon emission quotas are carried out. The numerical results show that the consensus cost of this method is better than the results under the stochastic programming method, and it brings new solutions to the group decision-making progress in the allocation of carbon emission quotas.