Adaptive and sparsest time-frequency analysis（ASTFA）is a new method for time-frequency analysis.ASTFA is lack of adaptivity as comparatively accurate initial values have to be set beforehand.Aiming to solve the problem existed in ASTFA，adaptive and sparsest time-frequency analysis method based on initial value optimization was proposed.The energy value of the residue is applied as the optimization objective function，and different initial values are used for signal decomposition.Initial values are considered to be the best only if the energy value of the corresponding residue is the smallest.Therefore，the adaptivity of ASTFA method is improved by the proposed method as the best initial values can be found adaptively. Simulation signal is applied to compare the proposed method and the initial ASTFA method.The results show that more accurate decomposition results can be adaptively obtained by using the proposed method.Analysis of simulation signal and rolling bearing fault signal shows that compared with empirical mode decomposition（EMD）method，the proposed method is superior at least in restraining end effect and mode mixing，anti-noise performance and gaining more accurate components.Meanwhile，the proposed method is effective in rolling bearing fault diagnosis.