Banana Fusarium wilt disease caused by Fusarium oxyspoum f. sp. cubense (Foc) seriously threatens the banana industry. Foc tropical race 4 (Foc TR4) can infect almost all banana cultivars. Compared with traditional physical and chemical practices, biocontrol strategy using beneficial microbes is considered as an environmentally sound option to manage fungal disease. In this study, a strain, H3-2, isolated from a non-infected banana orchard, exhibited high antifungal activity against Foc TR4. According to its morphological, physiological, and biochemical characteristics, the strain H3-2 was identified as Streptomyces sp. and convinced by the polymorphic phylogenic analysis of 16S rRNA sequences. Extracts of the strain H3-2 suppressed the growth and spore germination of Foc TR4 in vitro by destroying cell membrane integrity and mycelial ultrastructure. Notably, the strain and its extracts showed broad-spectrum antifungal activity against the selected seven fungal phytopathogens. Fourteen chemical compounds in the extracts were identified by gas chromatography–mass spectrometer (GC-MS), primarily phenolic compounds. Additional pot inoculation experiment demonstrated that the fermentation broth of the strain H3-2 promoted the growth of banana seedlings by efficiently inhibiting the spread of banana Fusarium wilt disease. This study demonstrated the potential application of the novel Streptomyces sp. H3-2 for the management of banana Fusarium wilt.