The critical current (I(c)) of high-temperature superconductor (HTS) tapes has to be examined not only for short samples, but also for the entire tape, because local weak points can possibly lead to the quenching of the whole HTS device. Some methods were reported for continuous I(c) measurement along the length of a HTS tape, but few of them were applicable to tapes with magnetic substrates represented by YBa2Cu3O(7-δ)(YBCO)-coated conductors based on Ni5W alloy substrate by rolling assisted bi-axially textured substrate process. We previously presented a contact-free method using magnetic circuits to measure I(c) continuously of long HTS tapes, namely the magnetic-circuit (MC) method. This method has been previously applied with high speed and resolution to measure I(c) of HTS tapes with non-magnetic substrates, due to its resistance to noise aroused by mechanical vibration. In this work, its ability to measure HTS tapes with magnetic substrates is demonstrated both theoretically and experimentally. A 100 m long commercial YBCO tape based on Ni5W alloy substrate was measured and regular I(c) fluctuations were discovered. The MC method can be a powerful tool for quality control of HTS tapes, especially for tapes with magnetic substrates.