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This paper presents current distributions consisting of transport and screening currents flowing in a YBCO coated conductor (CC) under flux densities of several tesla in liquid helium, where magnetic flux should be at center along a width of the CC. Distributions of magnetic flux densities generated by the currents in the CC were measured. In order to demonstrate the current distributions, a one dimensional inverse problem was solved using Tikhonov regularization. Sheet current density distributions near one edge with external field, where magnetic flux existed all over the width, were constant even if transport current increased. The constant current density corresponded to a critical current at the field divided by the width. Magnetic flux density distributions were asymmetric to the width of a CC under external magnetic flux density of several tesla. On the other hand, hysteresis of the magnetic flux densities above the CC shrank symmetrically to the width with increases of transport current.