Short-video recommendation is one of the most important recommendation applications in today's industrial information systems. Compared with other recommendation tasks, the enormous amount of feedback is the most typical characteristic. Specifically, in short-video recommendation, the easiest-to-collect user feedback is from the skipping behaviors, which leads to two critical challenges for the recommendation model. First, the skipping behavior reflects implicit user preferences, and thus it is challenging for interest extraction. Second, the kind of special feedback involves multiple objectives, such as total watching time, which is also very challenging. In this paper, we present our industrial solution in Kuaishou, which serves billion-level users every day. Specifically, we deploy a feedback-aware encoding module which well extracts user preference taking the impact of context into consideration. We further design a multi-objective prediction module which well distinguishes the relation and differences among different model objectives in the short-video recommendation. We conduct extensive online A/B testing, along with detailed and careful analysis, which verifies the effectiveness of our solution.