Hi Hwoarang,

This is an example with animate. It also shows the animate user interface in the animated gif:

slides = 1
qq =
  Table[
   Animate[Grid[
     {{Plot[x^2 + q^2 x, {x, 0, 10}, ImageSize -> 200, 
        PlotRange -> {{0, 10}, {0, 1500}}],
       Plot[(x + q)^2 + 2 x, {x, 0, 10}, ImageSize -> 200, 
        PlotRange -> {{0, 10}, {0, 1500}}]}}
     ], {{q, k/slides, "slider:"}, 5, 15}],
   {k, 5*slides, 15*slides}];
qq = Join[qq[[1 ;; Dimensions[qq][[1]] - 1]], Reverse[qq]]; 
Export["testmani.gif", qq, "DisplayDurations" -> 1];
SystemOpen[%]

There was a problem with this code. It worked fine in mma 9. In 10.0.2 and 10.1 the slider jumps in a strange way. This because i didn't use a fixed PlotRange. Now it works as expected.

hi hwoarang,
I think this is the animated gif you are looking for:

Export["e:\\folder\\animatedgif.gif",
 Table[
  GraphicsGrid[{{Plot[x^2 + q^2 x, {x, 0, 10}, ImageSize -> size], 
     Plot[(x + q)^2 + 2 x, {x, 0, 10}, ImageSize -> size]}}
   ],
  {q, 5}],
 "DisplayDurations" -> 0.5,
 Background -> LightBlue]

DisplayDurations is 1 picture each 0.5 second. In total 5 pictures by using Table.