High temperature superconducting (HTS) tri-axial CORC cable has been a potential candidate for the transmission line used in an all-electric aircraft because of its advantages such as compactness, high power density and reduced usage of HTS tapes. A tri-axial CORC HTS cable (10 MW, 3 kV/2 kA) is being developed in University of Bath in cooperating with Airbus. AC/DC converters, generators and motors will induce harmonic currents in the power system of a hybrid electrical aircraft. It may considerably affect the AC loss of the transmission cable, which is one of the key factors determining the efficiency of the cable. This paper studies the transport AC losses of this tri-axial CORC cable and the influence of harmonic current on the losses. A finite element method (FEM) model has been developed based on T-A formulation to analyze the dynamic electromagnetic behavior of this tri-axial CORC cable. Analyses are performed under rated load with & without harmonic currents. Results show that the transport AC loss has a significant non-uniform distribution among three phases even under a three-phase balanced load. A small harmonic current (less than 10 %) can considerably increase the AC loss of the tri-axial cable (up to 40 %).