Outsourcing heavy storage and computation to the cloud servers now becomes more and more popular. How to secure share the cloud storage is an important problem for many mobile users. Proxy re-encryption is such a cryptographic primitive which can be used to secure share cloud data. Until now there are many kinds of proxy re-encryption schemes with various properties, such as conditional proxy re-encryption, proxy re-encryption with keyword search etc. However until now there exists no work focus on proxy re-encryption for mobile cloud storage sharing. In mobile cloud storage, almost all the users are mobile ones, they only have resource-restricted equipments. In this paper we try to initialize this research, we give a very basic outsourced online/offline proxy re-encryption scheme for mobile cloud storage sharing and leave many interesting open problems as the future work. © Springer Nature Switzerland AG 2019.