New indole alkaloids streptoprenylindoles A–C (1–3) and diterpenoids 18-acetyl-cyclooctatin (8), 5,18-dihydroxy-cyclooctatin (9), and 5-dehydroxy-cyclooctatin (10) were isolated from the culture of marine-derived Streptomyces sp. ZZ820, along with known 3-cyanomethyl-6-[3-methyl-2-butenyl]indole (4), N-(2-(1H-indol-3-yl)ethylacetamide (5), 1-acetyl-β-carboline (6), indole-3-methylethanoate (7), cyclooctatin (11), and chromomycin A3 (12). Their structures were elucidated by a combination of extensive spectroscopic analyses, ECD calculation, and the Mosher's method. Streptoprenylindoles A (1) and B (2) are enantiomers that were separated through the preparation of their Mosher esters. Three new diterpenoids (8–10) showed antibacterial activities against methicillin-resistant Staphylococcus aureus (MRSA) and Escherichia coli with MIC values of 24.11–55.12 μM, while chromomycin A3 (12) showed potent antibacterial activities against MRSA (MIC: 0.59 μM) and E. coli (MIC 0.04 μM).