Big data is the term for a collection of datasets so huge and complex that it becomes difficult to be processed using on-hand theoretical models and technique tools. Brain big data is one of the most typical, important big data collected using powerful equipments of functional magnetic resonance imaging, multichannel electroencephalography, magnetoencephalography, Positron emission tomography, near infrared spectroscopic imaging, as well as other various devices. Granular computing with multiple granular layers, referred to as multi-granular computing (MGrC) for short hereafter, is an emerging computing paradigm of information processing, which simulates the multi-granular intelligent thinking model of human brain. It concerns the processing of complex information entities called information granules, which arise in the process of data abstraction and derivation of information and even knowledge from data. This paper analyzes three basic mechanisms of MGrC, namely granularity optimization, granularity conversion, and multi-granularity joint computation, and discusses the potential of introducing MGrC into intelligent processing of brain big data.