1. A method of authenticating a user of a terminal using an icon password, the terminal being connected to a server through an electronic communication network, wherein an icon database and an authentication database are connected to the server, the icon database storing a plurality of icons assigned with unique values and the authentication database storing authentication information including passwords of respective users, the method comprising: requesting an authentication to the server through the communication network (S 10 ), retrieving unique values and icons corresponding to the unique values from the icon database (S 20 ), creating a same number of assigned value as the retrieved unique value for each icon through a non-duplicate random number generation (S 30 ), transmitting the icon information containing the assigned values to the terminal through the communication network (S 40 ), implementing a password input screen based on the transmitted icon information (S 51 ), transmitting the authentication information containing assigned values of the selected icons to the server through the communication network (S 52 ), converting the assigned values contained in the transmitted authentication information to corresponding unique values (S 61 ), querying the authentication database using authentication information converted from the assigned values (S 62 ), and accepting the authentication request if the authentication information is valid (S 63 ).