•The recombinant T. maritima BfrA was covalently attached to Glyoxyl–Sepharose CL 4B.•We reached total retention of the enzymatic activity assisted by a rational design.•Immobilisation enhanced thermostability without variation in catalytic properties.•The biocatalyst hydrolysed concentrated sucrose solutions at a high temperature. Thermotoga maritima exo-β-fructosidase (BfrA) secreted by a recombinant Pichia pastoris strain was optimally immobilised on Glyoxyl–Sepharose CL 4B using the Rational Design of Immobilised Derivatives (RDID) strategy. Covalent attachment of the N-glycosylated BfrA onto the activated support at pH 10 allowed total recovery of the loaded enzyme and its activity. The immobilisation process caused no variation in the catalytic properties of the enzyme and allowed further enhancement of the thermal stability. Complete inversion of cane sugar (2.04M) in a batch stirred tank reactor at 60°C was achieved with a productivity of 22.2g of substrate hydrolysed/gram of biocatalyst/hour. Half-life of the immobilised enzyme of 5days at 60°C was determined in a continuously operated fixed-bed column reactor. Our results promote the applicability of the BfrA-immobilised biocatalyst for the complete hydrolysis of concentrated sucrose solutions under industrial conditions, especially at a high reaction temperature.