Poly(3-hydroxybutyrate-co-3-hydroxyvalerate-co-4-hydroxybutyrate) [P(3HB-co-3HV-co-4HB)] terpolymer was produced using Cupriavidus sp. USMAA2-4 via one-step cultivation process through combination of various carbon sources such as 1,4-butanediol or gamma-butyrolactone with either 1-pentanol, valeric acid, or 1-propanol. Oleic acid was added to increase the biomass production. The composition of 3HV and 4HB monomers were greatly affected by the concentration of 1,4-butanediol and 1-pentanol. Terpolymers with 3HV and 4HB molar fractions ranging from 2 to 41 mol.% and 5 to 31 mol.%, respectively, were produced by varying the concentration of carbon precursors. The thermal and mechanical properties of the terpolymers containing different proportions of the constituent monomers were characterized using gel permeation chromatography (GPC), DSC, and tensile machine. GPC analysis showed that the molecular weights (M (w)) of the terpolymer produced were within the range of 346 to 1,710 kDa. The monomer compositions of 3HV and 4HB were also found to have great influences on the thermal and mechanical properties of the terpolymer P(3HB-co-3HV-co-4HB) produced.