A promising solution for the near future is the substitution of non-renewable fossil fuels with sustainable liquid feedstock such as biofuel (biodiesel). The cost of conventional biodiesel production is higher than that of petroleum-based diesel production since it is produced mostly from expensive high-quality virgin oil. Conventionally, commercial biodiesel is produced via liquid phase base-catalyzed transesterification of the triglyceride components of the oil with short-chain alcohols. This study demonstrates the first effective conversion of the triglyceride, tristearin (TS) and the monoglyceride, glycerol monostearate (GMS) to biodiesel using novel protonated and then basified crosslinked modified polyacrylonitrile ion exchange fibres (PANF) in the form of a mesh and an investigation of their lifetime in batch recycling. 3 g of basified PANF in 26 mL of methanol with a molar ratio of methanol to tristearin (TS) of 274 : 1 at 65 °C could achieve 95% conversion of tristearin. The catalyst was re-used for 9 cycles (18 hours) before being effectively regenerated back to 70% conversion. Response surface methodology (RSM) with central composite design (CCD) gave an optimum biodiesel conversion of tristearin of 87.62% with 2.5 g of catalyst, methanol to TS molar ratio of 143 : 1 at 65 °C for 1 h (0.1936% error). Using glycerol monostearate at (a molar ratio of methanol to GMS of (115 : 1)) conversion to the methyl ester was above 97.63% at 65 °C in 60 min. These basified PANF ion exchange fibres showed comparable activity to conventional homogeneous base catalysts namely, NaOH; as well as exhibiting high stability and ease of use. The FT-IR spectra suggested that after use, active sites were blocked with most probably unreacted reactants which can be removed with a more extensive DCM washing regime. As PANF is produced in the form of a self-supporting mesh it is easy to use, regenerate in situ, maintain and replace in a continuous flow reactor. The study is promising as a basified catalyst for sustainable use in converting triglyceride (TGs) in fats, oils and greases (FOGs) and fatbergs in wastewater to biodiesel.