Isomaltose–oligosaccharides (IMOs), as food ingredients with prebiotic functionality, can be prepared via enzymatic synthesis using α-glucosidase. In the present study, the α-glucosidase (GSJ) from Geobacillus sp. strain HTA-462 was cloned and expressed in Escherichia coli BL21 (DE3). Recombinant GSJ was purified and biochemically characterized. The optimum temperature condition of the recombinant enzyme was 65 °C, and the half-life was 84 h at 60 °C, whereas the enzyme was active over the range of pH 6.0–10.0 with maximal activity at pH 7.0. The α-glucosidase activity in shake flasks reached 107.9 U/mL and using 4-Nitrophenyl β-D-glucopyranoside (pNPG) as substrate, the Km and Vmax values were 2.321 mM and 306.3 U/mg, respectively. The divalent ions Mn2+ and Ca2+ could improve GSJ activity by 32.1% and 13.8%. Moreover, the hydrolysis ability of recombinant α-glucosidase was almost the same as that of the commercial α-glucosidase (Bacillus stearothermophilus). In terms of the transglycosylation reaction, with 30% maltose syrup under the condition of 60 °C and pH 7.0, IMOs were synthesized with a conversion rate of 37%. These studies lay the basis for the industrial application of recombinant α-glucosidase.