We study the average-case learnability of DNF formulas in the model of learning from uniformly distributed random examples. We define a natural model of random monotone DNF formulas and give an efficient algorithm which with high probability can learn, for any fixed constant γ > 0, a random t-term monotone DNF for any t = O(n^{2 - γ}). We also define a model of random non-monotone DNF and give an efficient algorithm which with high probability can learn a random t-term DNF for any t = O(n^{3/2 - γ}). These are the first known algorithms that can learn a broad class of polynomial-size DNF in a reasonable average-case model of learning from random examples.