Given the singularity problem of the gesture password in speed dial gesture authentication, we can improve the program by adding a 1bit random number and some frequency variables, thus realizing the dynamic change of the authentication password. By improving the authentication process, the number of user authentication points is reduced and the convenience of the authentication mechanism is enhanced. The authentication process is improved as following: the number of authentication points is determined according to the random number and the starting point of the authentication is determined according to the last authentication point of the latest successful authentication (i.e., the authentication point adjacent to the last authentication point of the latest successful authentication is taken as the starting point of the authentication point). If the authentication fails for three times, the random number will be automatically updated. If the random number is updated twice due to the authentication failures, the mobile phone automatically sends its location to the specified mailbox. Finally, the convenience and security of the improved authentication method are analyzed through theory and experiment. Experiments show that the improved authentication method has better security and is more convenient.