This paper proposes a door access control system with mobile phones which allows off-line delegations of an access. A model of door access control with mobile phones is introduced, and then the delegation is formalized as a copy of a door-key. On the previous model, secure copy by off-line is realized using the essential idea of the proxy signature. Moreover, the proposed system is implemented on mobile phones, and then the execution time of a copy and a verification are estimated. As a result, it is shown that the proposed system is feasible.