Web users are confronted with the daunting challenges of creating, remembering, and using more and more strong passwords than ever before in order to protect their valuable assets on different websites. Password manager is one of the most popular approaches designed to address these challenges by saving users' passwords and later automatically filling the login forms on behalf of users. Fortunately, all the five most popular Web browsers have provided password managers as a useful built-in feature. Unfortunately, the designs of all those Browser-based Password Managers (BPMs) have severe security vulnerabilities. In this paper, we uncover the vulnerabilities of existing BPMs and analyze how they can be exploited by attackers to crack users' saved passwords. Moreover, we propose a novel Cloud-based Storage-Free BPM (CSF-BPM) design to achieve a high level of security with the desired confidentiality, integrity, and availability properties. We have implemented a CSFBPM system into Firefox and evaluated its correctness and performance. We believe CSF-BPM is a rational design that can also be integrated into other popular Web browsers.