Using a dynamic programming framework, in an intertemporal consumption-saving model with income uncertainty and durability, we have found a closed form solution for consumption. Also, the precautionary savings term arising from the riskiness of income is formally derived. With durability assumption, consumption has a higher response to permanent income than the one in the standard model, and also responds to a distributed lag of past permanent incomes with alternating signs. Furthermore, the effect of income uncertainty is greater on consumption relative to the case with time-separable preferences. That is, as the strength of durability increases, the level of precautionary savings against income uncertainty will be higher.