I have installed moodle version 2.3.1 and some coding customized .Now i want to upgrade moodle version 2.7 how to upgrade with existing customized source code.
What did you customise?
Personally (we often get asked to do just this) I would start by getting the code into Git and go from there. Roughly speaking...
1. Get an original copy of Moodle of exactly the same version you have based your changes on. You can do this by looking at the build date in version.php and then digging back through the changes to that file in https://github.com/moodle/moodle/tree/MOODLE_23_STABLE (this isn't so hard, but read the Git documentation)
2. When you've done that do a 'diff' (http://man.cx/diff(1) or https://www.kernel.org/pub/software/scm/git/docs/git-diff.html) between the 'clean' version and your version to see what the changes are and get a patch file.
3. Get a clean copy of 2.7, do a clean install (don't upgrade yet)
4. Apply the patches to 2.7. Test, check and fix all the weird problems you have just introduced.
5. Find all the 'update.txt' files in the Moodle code that apply to your changes. Read them and act as required.
6. Use this version of 2.7 with your changes to do the upgrade. Now fix all the new problems you will find.