There exists many security primitives which use an alphanumeric password which uses hard cryptographic methods. Also the users struggle to remember the password for various internet services and if the user has a same password for various services then it is insecure. To avoid this, graphical passwords are designed and made more secure, memorable and also easier to use since the user is going to just click certain passpoints rather than typing an alphanumeric password. However, this scheme has achieved a limited success and due to its simple architecture it is not used widely. Passpoints also suffer a major drawback of shoulder surfing attacks when the passpoints are exposed in front of others. So to improve the security of this system we introduce a new system called Passpoints for Random Similar Images (PRSIm). This system use a set of similar images and have a common passpoints from which the password is been derived. While logging in a user a random image is generated and displayed from which the user have to identify a common passpoints which is already registered. So the user clicks the passpoints to derive the password which confuses the attackers while we have multiple login in front of them. Thus it is more secure than any other passpoints scheme and also eliminates the shoulder surfing attacks which are analyzed and the results are been given.