The scale factor of a superconducting gravimeter (SG) is usually calibrated by using simultaneous and co-located gravity measurements with the FG5-type absolute gravimeter (AG). In this paper, another new kind of absolute gravimeter-cold atom gravimeter (CAG) is first reported to calibrate the SG. Five-day side-by-side gravity measurements have been carried out by using our CAG (NIM-AGRb-1) to calibrate the SG (iGrav-012) located at Changping Campus of the National Institute of Metrology (NIM) of China. A weighted least-squares method is applied to determine the scale factor and the result is given as (?928.01 ± 0.73) nm·s?2·V?1 with a precision of 0.79‰. We have demonstrated that a calibration precision of 1‰level can be achieved after 3 days of parallel observations at spring tide. The obtained calibration results are then compared with the previous calibration by FG5X-249, which shows that the calibration precision obtained by using NIM-AGRb-1 was slightly higher than FG5X-249 with the same time interval. The factors affecting the calibration precision are analyzed in the calibrations by means of different AGs. Finally, several calibration experiments for SG iGrav-012 are discussed. The final scale factor is estimated as (?927.58 ± 0.36) nm·s?2·V?1 with an accuracy of 0.39‰. Our main results demonstrate that the CAGs can be used for high-precision calibrations of SGs.