This paper presents a novel architecture of multi-granular stream optical burst switching (MGS-OBS), which enables an all-optical network to support sub-wavelength streaming traffic of diverse bandwidth granularities with guaranteed end-to-end delay and data loss rate. It shapes a sub-wavelength stream into a periodic burst train; and allows variable bit rate (VBR) streaming traffic with same source and destination to share the reserved bandwidth through statistical multiplexing. By adopting periodic advanced scheduling of burst trains, MGS-OBS substantially decreases recursive signaling processing in supporting sub-wavelength streaming traffic. MGS-OBS employs burst train reservation blocking recovery by time-shifting a blocked burst train. Performance of MGS-OBS is analyzed in terms of wavelength utilization and data loss rate, and the stream transmission failure rate. It is found that the performance of the MGS-OBS is compared favorably with other OBS schemes that target for efficient support of bursty traffic.