The coupled nonlinear differential equations are utilized to solve the loss spectrum of saturable absorber grating (SAG). Without laser cavity, the influences of the parameters of SAG on the filtering behavior of the gratings such as grating bandwidth, loss of the central frequency, sidemode suppression ratio (SMSR), etc. are investigated. Furthermore, the longitudinal mode SMSR in the presence of resonator cavity and the parameter regions for the improvement of the SMSR are discussed. The flat sidemode loss spectrum can be achieved when the length of the saturable absorber is almost one third of the fiber length in the cavity, and SMSR is 0.3~0.6 dB higher than that without a cavity when the length of the SAG is under a certain value due to the power of writing beam. Finally, the condition for the flat sidemode loss spectrum is validated elementally by a frequency-sweep method.