A nonvolatile, vegetable‐oil based chemical, acrylated epoxidized soybean oil (AESO) was investigated as a replacement of volatile and toxic styrene in one of commercial UPE resins styrene‐(PG‐MA) that is a mixture of styrene and a UPE plastic from propylene glycol and maleic anhydride (PG‐MA). Neither AESO nor PG‐MA was capable of forming a strong matrix, respectively, for glass fiber‐reinforced composites. However, a mixture of AESO and PG‐MA resulted in glass fiber‐reinforced AESO‐(PG‐MA) composites that were comparable or even superior to those from styrene‐(PG‐MA) in terms of the flexural and tensile properties. Effects of AESO contents on the mechanical and viscoelastic properties of the glass fiber‐reinforced AESO‐(PG‐MA) composites were investigated. Resin viscosity and resin pot life as a function of temperature were studied. The curing mechanism of the AESO‐(PG‐MA) resins is also discussed. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017, 134, 45056.