The butt-coupling between a semiconductor laser diode and a fiber Bragg grating external cavity acts a key roll on the laser characteristics. The scatter matrix method considering the butt-coupling efficiency is used to analyze the butt-coupling between them. It is found that the butt-coupling distance and coupling efficiency determine the laser characteristics. For strong feedback, the single lasing wavelength changes in the reflection bandwidth of the effective reflectivity (approximately the Bragg region of the fiber Bragg grating) as the distances change. For weak feedback condition, some different results are obtained. The SMSRs in the two conditions are presented and analyzed. These results can provide important design guidance of device parameters for the practical fabrication.