The transport loss generated by a high temperature superconducting coil (HTS) in an AC transmission process will affect the operational stability of the superconducting power equipment. However, under different self-field conditions, the influence of the oscillation waveform parameters and coil structure parameters on the transport loss still needs to be clarified. This article establishes a two-dimensional axisymmetric model with a single-pancake coil with a double strip winding as the research object. For four different oscillation waveforms—sine waves, square waves, triangular waves and sawtooth waves—the influence of four variables, namely, the transmission current amplitude, the coil radius, the number of turns of the coil, and the turn-to-turn spacing of the coil, on the transport loss of HTS coils is studied in detail. The results show that under the exact parameters of the coil, for the generated transport loss, the square wave is the largest, the sine wave is the second largest, and the sawtooth and triangular wave are the smallest. Under the same self-field condition, the transport loss can be reduced by increasing the coil radius, the number of turns of the coil, and the turn-to-turn spacing of the coil, in which if the number of turns of the single-pancake coil with a double strip winding is less than 14, the transport loss can be obviously reduced by increasing the number of turns of the coil. When the number of turns exceeds 14, it does little to reduce the transport loss. Research findings can confirm the investigation of the operational stability and design of HTS coils.