Conversion prediction plays a very important role in online display advertising since Cost-Per-Action (CPA) has become one of the primary campaign performance objectives in the industry. Unlike click prediction, there are different types of conversions in their nature, and each may be associated with different decisive factors. In this paper, we formulate conversion prediction as a multi-task learning problem, so that the prediction models for different types of conversions can be learned together. These models share feature representations, but have their specific parameters, providing the benefit of information-sharing across all tasks. We then propose Multi-Task Field-weighted Factorization Machine (MT-FwFM) to solve these tasks jointly. Our experiment results on real-world data set show that MT-FwFM outperforms other state-of-the-art algorithms such as Factorization Machines (FM) and Field-weighted Factorization Machines (FwFM) by 0.81% and 0.84% on two types of conversions.