Recently, Internet of Things (IoT) has raised as an important research area that combines the environmental sensing and machine learning capabilities to flourish the concept of smart spaces, in which intelligent and customized services can be provided to users in a smart manner. In smart spaces, one fundamental service that needs to be provided is accurate and unobtrusive user identification. In this work, to address this challenge, we propose a Gait Recognition as a Service (GRaaS) model, which is an instantiation of the traditional Sensing as a Service (S2aaS) model, and is specially deigned for user identification using gait in smart spaces. To illustrate the idea, a Radio Frequency Identification (RFID)-based gait recognition service is designed and implemented following the GRaaS concept. Novel tag selection algorithms and attention-based Long Short-term Memory (At-LSTM) models are designed to realize the device layer and edge layer, achieving a robust recognition with 96.3% accuracy. Extensive evaluations are provided, which show that the proposed service has accurate and robust performance and has great potential to support future smart space applications.