Four new cyclic pentapeptides, avellanins D–G (1–4), together with four known compounds (5–8), were isolated from a mangrove-derived Aspergillus fumigatus GXIMD 03099 fungus from Acanthus ilicifolius L. Their structures were elucidated by analysis of HRESIMS, NMR, and ESI-MS/MS data. Their absolute configurations were determined by X-ray diffraction analysis and Marfey’s method. Compounds 1–8 were screened for insecticidal and antibacterial activities. Compound 2 showed insecticidal activity against newly hatched larvae of Culex quinquefasciatus with an LC50 value of 86.6 µM; compound 4 had weak activity against Vibrio harveyi with an MIC value of 5.85 µM.