A dynamically tunable fiber filter realizing complex spectra of phase-shifted long period fiber gratings (LPFGs)is proposed and demonstrated experimentally. The principle of the filter is based on two acousto-optic coupling processes occurring simultaneously. The first coupling process acts as a normal LPFG, while the second makes the coupling direction of the first process change continuously, leading to a similar transmission spectrum with the phase-shifted LPFGs, in which the changing of coupling direction is realized by the discrete phase shifts of the index modulation. By adjusting the acoustic drive signals, its transmission spectrum can be dynamically tuned to realize the phase-shifted LPFGs spectra under different phase shift numbers and locations.