A newly synthesized solid acid catalyst SO42−/SnO2-diatomite was prepared for synthesizing furfural from corncob in the presence of homogeneous Brönsted acid. The relationship between pKa of Brönsted acid and turnover frequency (TOF) of co-catalysis with Brönsted acid plus SO42−/SnO2-diatomite was explored on the conversion of corncob to furfural. HCl (pKa = −7.0) (0.5 wt%) plus SO42−/SnO2-diatomite (3.6 wt%) gave the highest furfural yield (40.1%) with TOF value at 2.98 h−1 in the aqueous media. In the γ-valerolactone–water (6:4, v:v) biphasic media containing 15 g/L ZnCl2, one-pot conversion of corncob with co-catalysts gave a furfural yield of 68.9% at 170 °C for 30 min. Additionally, an efficient SO42−/SnO2-diatomite recycling was achieved with a productivity of 15.6 g furfural/(g solid acid·day) after 5 cycles of repeated use. Clearly, this one-pot co-catalysis process has high potential application for furfural production in future.