Abstract: To minimize the errors in the calibration of the fluxgate magnetometer with the David-Smith method, the error characteristics of the magnetic zero-offset determined by the Davis-Smith equation are simulated with the same magnetic field wave in different reference coordinate systems. It is found that the zero-offset error corresponding to the same wave in different coordinate systems can be very different. Selecting a specific coordinate reference system (relative to the field-aligned coordinate system) can effectively reduce the calculation error related to the Davis-Smith equation. The calculation error determined by using the data from two wave events tend to be significantly reduced compared with that by using a single wave event as the reference. Thus, the distribution characteristics of these zero-offset errors can be used for selecting an appropriate magnetic field wave period, thereby to improve the in-flight calibration accuracy of the fluxgate magnetometer.