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An eddy-current-based SQUID-NDE system has been developed to detect shallow surface defects of less than 50 mum in depth on heat-exchanger copper tubes using a HTS-SQUID and excitation coil. In this system, small surface displacement of a tube, variation of the tube thickness and inner ripples cause background magnetic noise besides the surface defects. In this study, main factors of the background magnetic noise were investigated by a HTS-SQUID gradiometer, laser displacement sensor and laser microscope. The magnetic response, surface displacement, outer diameter variation and radial thickness of straight tubes of 9.6 mm in outer diameter and 0.4 mm in thickness were measured. The experimental results suggested that the main factor of the background magnetic noise was not due to local shape displacement near the SQUID, but nonuniformity in tube shape mainly originated inside of the tube. In the case of a tube with inner ripples and a outer-surface defect, large periodical magnetic noise from ripples was measured. Noise reduction method to reduce the periodical magnetic background noise due to the inner ripple was also investigated. The periodical noise due to the ripples was significantly decreased at higher frequency than 300 kHz, where the skin depth into copper was about 0.1 mm, while the magnetic response from the defect of 30 mum in depth on the tube surface was successfully detected.