This paper introduces a method to measure critical current of high-temperature superconductor (HTS) tapes continuously using magnetic circuits. This method has two featured advantages. First, it is resistant to noises caused by mechanical vibration in principle, so high speed stable measurements are achieved; second, it can measure HTS tapes with magnetic substrates (e.g. RABiTS). In this paper, the principle of the method is introduced and the apparatus for kilometer-length HTS tapes measurements is constructed. Several Bi2223/Ag and YBCO tapes are measured to verify advantages of the method