Abstract: The β decays of atomic nuclei refer to the transformation that the nuclei emit a β particle or capture an electron. The accurate measurements of the β transition strength functions S_β(E) are of great significance in exploring the structure of unstable nuclei, revealing the process of stellar nucleosynthesis and also verifying the β decay theories. Experimentally, one way to determine the β transition strength is to directly measure the beta decay product using β-γ coincidence technique and/or total absorption spectroscopy. This method can give the transition information within the Q_β window. Another method to obtain the β decay strength is via the charge exchange reactions performed at the intermediate energy region (100~400 MeV/u), such as (p, n) or (³He, t). This is done by a high-precision measurement of the differential cross section. This method allows to access the transition strength that beyond the Q_β window, however, it is restricted by the beam intensity, and as a consequence hard to perform a systematical study of unstable nucleus with low yields. In view of this, in this paper we proposes a systematic measurement of the total charge exchange reaction cross section of the unstable nuclei. Combined with the well developed nuclear reaction theory, this method may set a constrain to the summed strength of the Gamow-Teller transition of the unstable nuclei within the proton separation threshold. Moreover, we introduce briefly the relevant work that has been carried out and planned.