Online display advertising has become a vital business for large-scale E-commerce markets. As the main goal of advertisers is to reach interested customer prospects, accurate conversion prediction is essential for successful online display advertising. A particular challenge for conversion prediction is that conversions may occur long after the click events. Such delayed feedback makes it a non-trivial task to keep conversion prediction models updated and consistent with the latest customer distribution. Although several studies have been conducted to tackle the delayed feedback issue, the relationship between the early conversion and full term conversion has not been fully exploited to improve conversion prediction. In this paper, we consider conversion prediction as a multi-task learning problem by leveraging multiple conversion labels after different observation intervals. Specifically, we propose a multi-task model with an end-to-end architecture for conversion prediction. Our approach is guided by theoretical and probabilistic analysis of the early and full term conversions. Our mixture-of-experts module can integrate distinct characteristics of input features and optimize the task-specific experts. In addition, the multiple tasks are jointly learned with a regularization term to ensure the embedding consistency between tasks and prevent potential overfitting issues. In comparison with competitive benchmarks, our approach can significantly improve conversion prediction with delayed feedback and improve business performance of online display advertising.