Thanks to all.. for their useful disscussion

How about

l1 = ListPlot[{{1, 0.0385}, {2, 0.04}, {3, 0.04096}, {4, 
    0.041044}, {5, 0.0408417}, {6, 0.0405}, {7, 0.04011}, {8, 
    0.03965}, {9, 0.0391528}, {10, 0.03861}}, Joined -> True]

l2 = ListPlot[{{1, 1.0386}, {2, 1.04029}, {3, 1.04108}, {4, 
    1.04113}, {5, 1.04091}, {6, 1.04056}, {7, 1.04015}, {8, 
    1.03969}, {9, 1.03918}, {10, 1.03864}}, Joined -> True]

Column[{l1, l2}]

Thanks Simon.. But Method does not gives the accurate figure.. Because In this Way Both the Graphs of List1 and LIst2 looses their original shape.

Show[{
  ListPlot[List1, Joined->True], 
  ListPlot[Map[# - {0, .997} &, List2], Joined->True]
 }, PlotRange->All, Axes->{True, False}]

Look up each of those words in the help system and study them until you can understand how and why this was done.