The yield of copolymerization of tetrahydrofuran and propylene oxide (THF:PO=100:5—15, by wt.) using a binary catalyst of fuming sulfuric acid (21% or 28%) and perchloric acid is around 50—60%, and the loss of THF in the reaction is below 10—15%. The average molecular weight of the product can be controlled in the range of 1000—2000 by varying the binary catalyst system. The present method, which is different from the usual copolymerization initiated by BF3-diol or SbCl5-diol system, shows the pecularities i.e.the yield of copolymerization with the low PO feed is not decreased,the hydroxyl funcitonality is equal to 2,and the end-groups are predominantly primary hydroxyls(around 65-70%).