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 megahertzs over 100 nm bandwidth range with high signal-to-noise ratio (SNR) and good flatness output. A steady-state model and segmentation algorithms are employed to investigate the gain spectra of the SOA and the laser wavelength of the SOA-RL when the SOA is driven by some non-uniform injections, such as linear, quadratic, exponential, or square root functions. The results show that the laser wavelength changes slowly with the change of injection current when its average is greater, and there is a minimum value when the injection current is exponentially distributed along the SOA, which exhibits high wavelength stability.