This paper introduces a new method for adaptively estimating the time-varying autocorrelation (TV-AC) of nonstationary signals and studies its application to time-frequency analysis. The proposed method employs local estimation with a sliding window having a certain bandwidth to estimate the TV-AC locally. The window bandwidths are selected adaptively by a local plug-in rule to address the bias and variance tradeoff problem. Further, based on the proposed adaptive TV-AC estimation, a new time-frequency analysis method called adaptive windowed minimum variance spectral estimation (AWMVSE) is developed. Simulation results show that the proposed adaptive TV-AC estimation method and AWMVSE method have improved performances over conventional estimators with a fixed window.