Got reason of the problem, it was gnutls package. It's working weird behind a proxy. But openssl is working fine even in weak network. So workaround is that we should compile git with openssl. To do this, run the following commands:
sudo apt-get update
sudo apt-get install build-essential fakeroot dpkg-dev
sudo apt-get build-dep git
mkdir ~/git-openssl
cd ~/git-openssl
apt-get source git
dpkg-source -x git_1.7.9.5-1.dsc
cd git-1.7.9.5
(Remember to replace 1.7.9.5 with the actual version of git in your system.)
Then, edit debian/control file (run the command: gksu gedit debian/control) and replace all instances of libcurl4-gnutls-dev with libcurl4-openssl-dev.
Then build the package (if it's failing on test, you can remove the line TEST=test from the file debian/rules):
sudo apt-get install libcurl4-openssl-dev
sudo dpkg-buildpackage -rfakeroot -b
Install new package:
i386: sudo dpkg -i ../git_1.7.9.5-1_i386.deb
x86_64: sudo dpkg -i ../git_1.7.9.5-1_amd64.deb
Inspired from here: https://github.com/xmendez/wfuzz/wiki/PyCurlSSLBug