Absorption and emission cross sections are the key parameters of the erbium-doped fiber super fluorescent source (EFSFS). They form the foundation of theoretical spectrum analysis including mean wavelength stability. In pervious works those parameters were usually determined by loss or gain spectra measurement with a broad band light source (BBS) and an optical spectrum analyzer (OSA). Though the absorption or emission cross sections all over the whole wavelength range can be acquired at the same time, the popular method suffers from low precision due to the crosstalk between different wavelengths transmitted in the fiber. As an improvement, in this paper the measurement was conducted based on a point-by-point wavelength sweep method with a tunable laser near 1550nm and a power meter. That provides the access to accurate simulation of the EFSFS spectrum, which reveals that the left peak around 1530nm of the single-pass backward (SPB) configuration has superior mean wavelength stability against temperature variation. Moreover, the performance can be further improved by a narrow optical filter. The mean wavelength shift range is suppressed to 1 part per million (ppm) when the bandwidth is under 2nm. Those conclusions are expected to be applied to design of EFSFS for the fiber optic gyroscope (FOG) in the future.