First if you want to update the homebrew to the recent version you can use this command:
brew update
But recently I got a error message when I run this command:
Error: /usr/local must be writable!
It seems like I do not have the permission to access this directory. Indeed I do not have the permission of this directory, because this directory belongs to wheel group.
After google some solutions, I solved this by the following method:
Change the group and give a write permission of this directory and all the sub files or directory with this two command.
sudo chgrp -R admin /usr/local
sudo chmod -R g+x /usr/local
Then run the brew update.
That's all.