We investigate the translocation of single polymer chain through a nanopore located on a membrane with different solvents in the two sides of the membrane. For the case under study, the effect of solvents on the translocation dynamics is significant, and as a result, the mean first passage time shortens remarkably compared with that calculated in the case of good solvents on both the sides of the membrane. In addition, we also discuss the condition such that the present result holds true.