The fiber ring laser based on the semiconductor optical amplifier (SOA) is widely used for optical communications and optical fiber sensing, because it can be tuned at an ultra high speed up to Mega hertz. The steady-state model and segmentation algorithm are employed to study the amplified spontaneous emission (ASE) properties of the SOA, then two kinds of the tunable ring lasers based on SOA (SOA-TRL) are investigated with the Gaussian or Fabry-Perot (F-P) filter. The evolutions of the output spectra and the peak power are demonstrated with the round trip of the light traveling in the ring cavity, which show the lasing process from the ASE to laser. It shows that the F-P filter can improve the wavelength tuning speed because the SOA-TRL with an F-P filter can establish the laser within only a few round trips, and it could be designed for some high speed applications.