Many of current spoken dialog systems can conduct non-task-oriented dialog. The systems that can improve user impression are required for users to keep using them. This paper focuses on self-disclosure, that is a process that a person reveals information about herself/himself to an interlocutor in human-human conversation. It is known that the self-disclosure plays a vital role to develop an intimate relationship. However, it is still unclear how exchanging the self-disclosures affects the user impression in the human-machine dialog. In this paper, we conduct dialog experiments to investigate the effectiveness of mutual self-disclosures between the user and the system. To achieve this goal, we built a spoken dialog system which conducts the dialog that the user and the system disclose information about themselves alternately. The dialog experiments revealed that the proposed system can improve the user impression regarding satisfaction and friendliness.