Housing demand estimation is an important topic in the field of economic research. It is beneficial and helpful for various applications including real estate market regulation and urban planning, and therefore is crucial for both real estate investors and government administrators. Meanwhile, given the rapid development of the express industry, abundant useful information is embedded in express delivery records, which is helpful for researchers in profiling urban life patterns. The express delivery behaviors of the residents in a residential community can reflect the housing demand to some extent. Although housing demand has been analyzed in previous studies, its estimation has not been very good, and the subject remains under explored. To this end, in this article, we propose a systematic housing demand estimation method based on express delivery data. First, the express delivery records are aggregated on the community scale with the use of clustering methods, and the missing values in the records are completed. Then, various features are extracted from a less sparse dataset considering both the probability of residential mobility and the attractiveness of residential communities. In addition, given that the correlations between different districts can influence the performances of the inference model, the commonalities and differences of different districts are considered. After obtaining the features and correlations between different districts being obtained, the housing demand is estimated by using a multi-task learning method based on neural networks. The experimental results for real-world data show that the proposed model is effective at estimating the housing demand at the residential community level.