Abstract: Domain adversarial adaptation in a continual setting poses significant challenges due to the limitations of accessing previous source domain data. Despite extensive research in continual learning, adversarial adaptation cannot be effectively accomplished using only a small number of stored source domain data, a standard setting in memory replay approaches. This limitation arises from the erroneous empirical estimation of $\mathcal{H}$-divergence with few source domain samples. To tackle this problem, we propose a double-head discriminator algorithm by introducing an addition source-only domain discriminator trained solely on the source learning phase. We prove that by introducing a pre-trained source-only domain discriminator, the empirical estimation error of $\mathcal{H}$-divergence related adversarial loss is reduced from the source domain side. Further experiments on existing domain adaptation benchmarks show that our proposed algorithm achieves more than 2$\%$ improvement on all categories of target domain adaptation tasks while significantly mitigating the forgetting of the source domain.