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Current carrying capabilities of HTS tapes and coils can be defined by critical current when carrying DC current. While there is no standard criterion to judge their AC current carrying capability. In actual industrial applications, HTS tapes and coils often need to work in AC conditions. Accurately calculating the current carrying ability of tapes and coils is a precondition of designing a HTS machine. DC and AC V - I properties are measured using four-probe method under different background magnetic field. The method of measuring and obtaining the AC maximum working current is given. The applicability of the method and phenomenon of experiment is discussed based on the Anderson-Kim flux creep model. The content of this paper moderately contributes to the completion of superconducting technology. And the paper can be referenced when designing HTS machine with HTS tapes or coils carrying AC current.