From the website http://www.if-not-true-then-false.com, I found the solution of solving the problem that Adobe Flash Player does not work on 64-bit Fedora 14. I followed the steps as below.
Firstly, remove any currently installed Flash Player
# yum remove flash-plugin nspluginwrapper* -y
Secondly, download Adobe Flash Player tarball and untar it
# cd /tmp
# wget http://download.macromedia.com/pub/labs/flashplayer10/flashplayer_square_p2_64bit_linux_092710.tar.gz
# tar -xzvf flashplayer_square_p2_64bit_linux_092710.tar.gz
Finally, move plugins to /usr/lib64/mozilla/plugins/ directory
# mv /tmp/libflashplayer.so /usr/lib64/mozilla/plugins/
Close the Firefox browser(if it opens), and open it to verify. It worked.