Sudo password doesn't work even if I have no password
sudo requires a password by default on Mac OS X.

Apple's knowledge base article explains more, Mac OS X: sudo command requires a non-blank admin password:


  In Mac OS X v10.5 through 10.5.8, if you press the Return key at the
  password prompt without entering a password (even if the user has no
  password, which is not recommended), the command entered will not
  execute and you will be returned to a command prompt.
  
  In Mac OS X v10.6 or later, if you press the Return key at the
  password prompt without entering a password, the message "Sorry, try
  again." will be displayed and you will be prompted for a password
  again.
  
  If your administrator account has no password (a blank password),
  you must give that user a password before using the sudo command.


If you must remove the need for a password to use sudo, you can edit the /etc/sudoers file using visudo command. A thread on macoshints discusses how:


  Use the visudo command as root.
  
  Look for the line:
  
  %admin  ALL=(ALL) ALL
  
  Change it to:
  
  %admin  ALL=(ALL) NOPASSWD: ALL


Requiring a password is highly recommended. Removing this check reduces the security of your Mac and exposes your computer to attack or abuse.