In this paper, we propose an adaptive STFT (ASTFT) with adaptive chirp-modulated Gaussian window. The window is obtained from rotating Gaussian function in time-frequency plane by fractional Fourier transform (FRFT). It is completely adaptive where the two parameters, FRFT rotation angle and Gaussian variance, are signal-dependent. The angle dependents on the chirp rate of the signal. The variance is determined by the chirp rate and its first derivative. Considering the input may be multicomponent, a chirp-modulated Gaussian window with time-frequency-varying angle and variance is developed. The proposed ASTFT has very high energy concentration and less interference between components in noiseless and noisy environments.