This paper describes a refined rf-SQUID magnetometer in which not only the fabrication of the SQUID sensor becomes easier but also the magnetic flux could be stably measured with sufficient sensitivity at a wider range of temperatures compared with existing SQUID systems. Two frequency components are used in the proposed rf-SQUID magnetometer, one of which is to excite the SQUID sensor and the other is to detect its response. Furthermore, from both the phenomenological analysis and the experimental results it is shown that the present rf-SQUID magnetometer performs its function well even if the value of LIc of the SQUID sensor is much larger than the flux quantum φ0.