Fungi are considered good producers of industrially valuable enzymes with higher enzymatic activities. Among these cellulases are group of extracellular enzymes commonly employed in many industries for the hydrolysis of cellulolytic material. Aspergillus fumigatus produced exoglucanase having high enzymatic activity (83 U/gds) during the solid-state fermentation of wheat straw under optimum physical and nutritional conditions. Maximum production was obtained after 72 h of fermentation, at 55 °C temperature, pH 5.5, 80 % moisture level, and 2 mL fungal inoculum. Production was further increased by the addition of fructose (0.3 %) as additional carbon source, peptone (0.4 %) as nitrogen source, Tween-80 (0.3 %) as surfactant, and ammonium sulfate (0.2 %) in media. Exoglucanase was 2.30-folds purified by adding 40 % ammonium sulfate with volumetric activity 95.4 U/gds and specific activity 14.74 U/mg. Further, it was 5.18-folds purified by gel filtration chromatography with volumetric activity 115.2 U/gds and specific activity 33.10 U/mg. Purified exoglucanase has maximum activity at 55 °C and pH 4.8 using 1 % Avicel aqueous solution as substrate. The K(m) and V(max) were 4.34 mM and 7.29 μM/min, respectively. Calcium, magnesium, and zinc ions have positive effect on exoglucanase activity.