Tunable narrow-band filters have important potential applications in optical communication and optical sensing systems.Especially,fiber grating based tunable narrow-band filters can find vary important applications in tunable narrow linewidth fiber lasers due to its simplicity,lower cost,and wide tuning range.In this thesis,sampled fiber grating based tunable narrow-band filters for tunable fiber laser applications were theoretically and numerically studied in details.The main works are as follows:1) The coupled-mode equations for fiber gratings and its numerical implementation methods were derived in details,based on which,the effects of various device parameters(such as the length of grating,the sampling period, duty cycle of rectangular function,the refractive index modulation intensity, etc.) and technologies(such as apodization,chirp,etc.) on the spectral characteristics of sampled fiber Bragg gratings were studied and simulated,and the key factors that impact the center wavelength,channel spacing,the 3dB bandwidth of reflection spectrum envelope of the sampled grating reflection were obtained.2) The stress and temperature tuning technologies for fiber gratings were theoretically analyzed and compared in details.3) The sampling functions and parameters for rectangle-sampled fiber Bragg grating and sine-sampled fiber Bragg grating were optimized and designed.As a result,a sampled fiber grating with 32nm of the 3dB bandwidth of reflection spectrum envelope and 76 wavelength channels was designed.4) The spectral and tuning characteristics of combined tunable narrow-band filter, formed by two different sampled fiber gratings were deeply studied.And its applications in tunable narrow linewidth lasers were analyzed and simulated. This thesis contains 71 pictures,1 table,and 59 references in total.