Federated recommender systems have distinct advantages in terms of privacy protection over traditional recommender systems that are centralized at a data center. With the widespread use and the growing computing power of mobile devices, it is becoming increasingly feasible to store and process data locally on the devices and to train recommender models in a federated manner. However, previous work on federated recommender systems does not fully account for the limitations in terms of storage, RAM, energy and communication bandwidth in a mobile environment. The scales of the models proposed are too large to be easily run on mobile devices. Also, existing federated recommender systems need to fine-tune recommendation models on each device, which makes it hard to effectively exploit collaborative filtering information among users/devices.Our goal in this paper is to design a novel federated learning framework for rating prediction (RP) for mobile environments that operates on par with state-of-the-art fully centralized RP methods. To this end, we introduce a federated matrix factorization (MF) framework, named meta matrix factorization (MetaMF), that is able to generate private item embeddings and RP models with a meta network. Given a user, we first obtain a collaborative vector by collecting useful information with a collaborative memory module. Then, we employ a meta recommender module to generate private item embeddings and a RP model based on the collaborative vector in the server. To address the challenge of generating a large number of high-dimensional item embeddings, we devise a rise-dimensional generation strategy that first generates a low-dimensional item * Co-corresponding author.