In this study, barium-terephthalate metal-organic framework (Ba(BDC)) was synthesized as a new efficient adsorbent by an aqueous media method. Terephthalate ligand recovered from polyethylene terephthalate (PET) waste was used as a precursor in the synthesis process. Infrared spectroscopy (FTIR), X-ray diffraction (XRD), energy-dispersive X-ray (EDX), and field-emission scanning electron microscopy (FESEM) were applied to analyze the chemical and crystal structure of Ba(BDC). For the first time, the adsorption ability of this compound was investigated to remove sulfate ions from water. Experimental design optimization approach involving both screening the effective factors (i.e. pH, adsorbent dosage (m), initial concentration of sulfate ion (C), and temperature (T), except contact time (t)) and running Doehlert design was led to obtaining a regression model for the relation between the removal percent of sulfate ion (R%) and four effective factors as follows √(R%)= 0.366 pH - 0.01328 C + 3.641 m + 0.2589 T - 0.02248 〖pH〗^2 +0.000003 C^2 -0.2991 m^2 - 0.003452 T^2 + 0.000437 pH×C - 0.01377 pH×T - 0.001821 C×m + 0.000102 C×T The resulting model was employed for finding optimum conditions including T= 29 °C, pH= 2, m= 3.1 mg and C = 200 mg˖L-1 that maximize R% of sulfate ion to 99.43 value. Furthermore, kinetics, isotherms, and thermodynamics studies are complementary divisions of this research. Because of a non-linear R2 value closer to 1 (R2 = 0.9831), the Langmuir-Freundlich isotherm model better describes the adsorbent-adsorbate behavior and its maximum adsorption capacity is qmax of 549.5 mg∙g-1. The kinetic experimental data obey the pseudo-second-order model (R2 = 0.9984). Based on the negative value of thermodynamic parameters including ∆H°, ∆S°, and ∆G°, the adsorption process is exothermic and spontaneous chemisorption at various temperatures (298, 308, 318, and 328 K).