Although it depends on the reason you are going to password your browser but that's my own reason which i have mentioned above, it's only for Google Chrome.
I RECOMMEND:- Mozilla Firefox, Opera, Safari And More Google Chrome Tips & Tricks
How To Password Your Chrome Browser With Secure Profile
1. Firstly launch your Google Chrome browser and CLICK HERE.
2. Then install the Chrome Extension And Enable it
3. Set Your Secure Profile Password And Note that Case Sensitive
4. Then when next you open your Chrome browser it will ask you for the password

5. That's all it will make your Browser Private to you alone.