When I use Command + t to open an new tab in terminal, it always open my home directory.
How can I new a tab which open the same directory?
As of Mac OS X Lion 10.7, Terminal will do this by default if you're using bash as your shell (which is the default).
You can set preferences to decide whether to have new tabs and/or windows open at the same directory as the current terminal:
Terminal > Preferences > Startup > New windows/tabs open with > Same Working Directory
This works by having your shell (or other programs) send an escape sequence to tell Terminal the current working directory. The code to do this is in the system-wide bash configuration file /etc/bashrc.
If you're using zsh, I've adapted and expanded the code for /etc/zshrc in my answer to Resume Zsh-Terminal (OS X Lion).
command + t
(for tab)
Typing in more to satisfy Stackoverflow's requirement that Body is at least 30 characters.
I would suggest you to use iTerm 2 and learn more about customizing it to your needs
On MAC 10
Terminal > Preferences > General>
change follow attributes to
New windows open with > Same Working Directory
New tabs open with > Same Working Directory
To apply change press command + T