Semiconductor optical amplifier-based ring cavity laser (SOA-RL), which has been widely used in optical communications, optical fiber sensing, and bio-photonics fields, can be tuned at an ultra high speed up to Mega Hertz over 100 nm bandwidth range with high SNR and flatness output. A steady-state model and segmentation algorithms are employed to investigate the gain spectra of four kinds of non-uniform SOA and the lasing wavelength of the SOA-RL. It shows that the dependence of the lasing wavelength on the average width is stronger when the light propagates from narrower to wider end than conversely, and there are some particular structures to show ultra high stability lasing wavelength. It is supposed that the main reason could be the carrier density distribution along the propagation.