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How do I convert the following image graph into data (if possible into function)?

enter image description here

I checked this answer and found that my problem is grid and plot have same color.

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If the problem is only to remove the grid, that's relatively easy. You just remove everything but the grid, then take the difference.

You can use Closing with a rectangular structuring element to remove everything but the horizontal / vertical grid lines, like this:

img = Import["http://i.stack.imgur.com/TkvSR.png"];    
hFilter = Closing[img, BoxMatrix[{10, 0}]];
vFilter = Closing[img, BoxMatrix[{0, 10}]];

then take the pixel-wise min to get the full grid:

grid = ImageApply[Min, {hFilter, vFilter}];

enter image description here

Then simply binarize the difference:

Binarize[ImageDifference[img, grid]]

enter image description here

(From here, you should be able to use code from the answers already linked.)

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