The continued development in the design technology of practical superconducting devices adopting high temperature superconductors tapes has led to a deeper understanding of their electromechanical behaviors. Rare-earth-barium-copper-oxide coated conductor (CC) tapes exhibit anisotropy of transport property (Ic) under magnetic field and its intrinsic strain effect is much significant depending on the orientation to the tape surface and the magnetic field intensity applied. Different experimental systems have already been developed to measure the relation of Ic with mechanical strain ε, magnetic field intensity B, and its angle of orientation, θ. However, few systems and instruments can measure these relationships simultaneously; either Ic-B-θ or Ic-ε-B is usually measured. In this study, a device which can measure these influences simultaneously based on a pair of permanent magnet systems was constructed and the characteristic responses of critical current Ic with strain, magnetic field, and its orientation with respect to the CC tape surface were investigated. The angular dependence of Ic with strain at 77 K in reactive co-evaporation by deposition and reaction GdBCO CC tapes has been measured using the permanent magnet system. The orientation angle of magnetic field with respect to the tape's surface was varied by rotating the rig fixture that holds a pair of permanent magnets. The strain sensitivity of Ic at different angles under low magnetic field was evaluated. As a result, a characteristic surface Ic (ε, θ, B) has been constructed as the characteristic response of Ic with strain and varying orientation under magnetic field.