Abstract We set up a model with inter-generational bequest transfers and a climate damage on the wealth of heterogeneous households. We show that, under the imperfections of credit markets and depending on the wealth distribution across households, a balanced budget climate policy may widen the wealth inequality between the rich and the poor class. A climate policy may create positive effects on the wealth of households but these effects are asymmetric across households in terms of both magnitudes and the transmissions of the gains from climate policy within households. The poor's gains from the climate policy are mainly transmitted into improving the living standard and then to invest in human capital because of the higher marginal return to education investment. In contrary, the rich's gains from the climate policy are transmitted biasedly into physical capital accumulation and enhance their monopoly position in producing intermediate inputs. We show that, for any climate policy, there exists a corresponding threshold of aggregate physical capital. When the aggregate physical capital of the economy exceeds this threshold then the corresponding climate policy may widen the inter-generational bequest transfers among heterogeneous households, therefore, contributing enlarge the wealth gap between the rich and the poor class in the long run.