I created a graph with Wolfram Mathematica and exported it as .eps file. Then I want to open it with Illustrator to do some amendment. But when I read it with Illustrator, it gives me an error：MPS analytic program can not analyse this file. How can I resolve it? I doubt it is due to the resolution because the other simpler graph(.eps) can be opened by Illustrator.
Place figure instead of importing
Illustrator is able to place EPS and PDF figures inside of a document without importing them. If you only need to add some elements to the figure and you do not need to edit it, this feature allows to avoid all the headache associated with importing it into Illustrator in the editable form.
Note that CorelDRAW is also able to place EPS, but this functionality currently (version X6) is still buggy and of little use.
Use another intermediate vector format
It is usually better to
Export figures from Mathematica as PDF for the purposes of importing them into such programs as Illustrator, CorelDRAW or Inkscape. From my experience the PDF format is the most supported vector format in Mathematica.
In the cases when PDF gives inappropriate results one can try
Exporting into EMF or SVG. Sometimes none of these solutions gives appropriate result but every of them allows to import correctly a subset of the original objects from Mathematica into vector drawing program. In such situations the correct result often can be obtained by combining correctly imported objects obtained through different intermediate vector drawing formats.
See also this answer for an explanation of differences between vector formats.
You should try to use a PDF export instead of EPS, it should do the same thing except that it should work better with transparencies etc. While so far i have mostly the same answer as Alexey Popkov who is worth listening to theres something more you can do:
In the case that you absolutely have to have an EPS file and none of the other files work, you can try to circulate the file trough eps2eps that comes with GhostScript. It will make your file simpler but will give it a much better chance of not failing.
Another approach is to convert the eps to PDF with acrobat distiller this works slightly better in some corner cases.
You should try exporting to SVG instead: here is how.