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Skin lesion segmentation is a crucial step in the computer-aided diagnosis of dermoscopic images. In the last few years, deep learning based semantic segmentation methods have significantly advanced the skin lesion segmentation results. However, the current performance is still unsatisfactory due to some challenging factors such as large variety of lesion scale and ambiguous difference between lesion region and background. In this paper, we propose a simple yet effective framework, named Dual Objective Networks (DONet), to improve the skin lesion segmentation. Our DONet adopts two symmetric decoders to produce different predictions for approaching different objectives. Concretely, the two objectives are actually defined by different loss functions. In this way, the two decoders are encouraged to produce differentiated probability maps to match different optimization targets, resulting in complementary predictions accordingly. The complementary information learned by these two objectives are further aggregated together to make the final prediction, by which the uncertainty existing in segmentation maps can be significantly alleviated. Besides, to address the challenge of large variety of lesion scales and shapes in dermoscopic images, we additionally propose a recurrent context encoding module (RCEM) to model the complex correlation among skin lesions, where the features with different scale contexts are efficiently integrated to form a more robust representation. Extensive experiments on two popular benchmarks well demonstrate the effectiveness of the proposed DONet. In particular, our DONet achieves 0.881 and 0.931 dice score on ISIC 2018 and $\text{PH}^2$, respectively. Code will be made public available.