Fine-grained urban flow inference, which aims to infer the fine-grained urban flows of a city given the coarse-grained urban flow observations, is critically important to various smart city related applications such as urban planning and public safety. Previous works assume that the urban flow monitoring sensors are evenly distributed in space for data collection and thus the observed urban flows are complete. However, in real-world scenarios, sensors are usually unevenly deployed in space. For example, the traffic cameras are mostly deployed at the crossroads and central areas of a city, but less likely to be deployed in suburb. The data scarcity issue poses great challenges to existing methods for accurately inferring the fine-grained urban flows, because they require all urban flow observations to be available. In this paper, we make the first attempt to infer fine-grained urban flows based on the incomplete coarse-grained urban flow observations, and propose a Multi-Task urban flow Completion and Super-Resolution network (MT-CSR for short) to simultaneously complete the coarse-grained urban flows and infer the fine-grained flows. Specifically, MT-CSR consists of the data completion network (CMPNet for short) and data super-resolution network (SRNet for short). CmpNet is composed of a local spatial information based data completion module LocCmp and an auxiliary information based data completion module AuxCmp to consider both the local geographical and global semantic correlations for urban flow data completion. SRNet is designed to capture the complex associations between fine-and coarse-grained urban flows and upsample the coarse-grained data by stacking the designed super-resolution blocks. To gain an accurate inference, two parts are jointly conducted under a multi-task learning framework, and trained in an end-to-end manner using a two-stage training strategy. Extensive experiments on four large real-world datasets validate the effectiveness and efficiency of our method compared with the state-of-the-art baselines.