Linewidth measurement of semiconductor laser always uses the heterodyne technology and the linewidth is confirmed with the power spectral density function of the beat signal. According this method, linewidth depends on the power spectral density function confirmed with Fourier transform, but the power spectral density function only defining for the wide-sense stationary signals can not apply to the unstable signals such as the beat signals. Fourier transform is a global transformation losing temporal information, so the dynamic or instantaneous linewidth getting through the power spectral density function is a stable value or a dynamic point in a period of time but not a instantaneous one. In order to contain the instantaneous linewidth of the semiconductor laser in the tuning process, the coherent and the incoherent measuring methods based on the time-varying power spectrum is proposed. The instantaneous linewidth measuring method based on time varying power spectrum has two ways according the time delay, the tuning instantaneous linewidth can be learned by building time varying power spectrum of the beat signals or the laser through doing time-frequency analysis to the beat signals. When doing time-frequency analysis, the beat signals must be decomposed to several mono-component signals firstly because the beat signals are typical non-stationary multi-component signals, and only when the signal is a mono-component signal, has the instantaneous frequency a clear and justifiable physical interpretation. However, the precision of decomposition algorithms is affected seriously by a main slow-varying tendency which changes as a sine or a frequency-modulated wave superimposing the beat signals, and the trend is so legible that it can be obtained in advance, so we propose the Tendency Local Mean Decomposition (TLMD) algorithm combining trend pre-extraction and Local Mean Decomposition (LMD) method which brings more excellence to decompose the beat signals. The time-varying power spectrums of the beat signal and the laser by using the product functions come from decomposition have been built, and the instantaneous linewidth of the distributed feedback semiconductor laser tuned by a sawtooth wave current of 50~51 and 50~100 mA has been obtained finally.