A connector and a connecting structure of a flexible flat cable are provided. The connector includes a main body, an electrical terminal and a cover plate. The main body has a sidewall and a boss. The sidewall and the boss define a groove therebetween. The electrical terminal is in a bent shape. One end of the electrical terminal is disposed on the boss. The cover plate has a cover portion and an engaging portion. The cover portion covers on the boss. The engaging portion is inserted into the groove of the main body. The electrical terminal is partially located between the boss and the cover plate. The present invention further provides the connecting structure of a flexible flat cable. The advantage of the present invention is that: by disposing the groove on the main body, the cover plate is inserted into the groove for engaging the flexible flat cable connected to the connector, thereby preventing the flexible flat cable from releasing from connector to increasing the mounting reliability.