An elastic cord unit includes a hollow outer elastic cord having a first longitudinal hole and two ends. Two first stops are respectively and securely received in the ends of the outer elastic cord. A hollow inner elastic cord is received in the outer elastic cord and includes a second longitudinal hole. Two ends of the inner elastic cord are respectively received in the first stops. Two second stops are respectively received in the ends of the inner elastic cord. Each end of the inner elastic cord is securely clamped between one of the first stops and one of the second stops. When the outer elastic cord breaks while a user is stretching the elastic cord unit, the inner elastic cord does not break to avoid injury to the user.