A filter can be analyzed by Bode plot of its magnitude and phase in a range of frequency. So far as I know, its phase has a non-zero phase. I am looking for the possibility of filter design which the phase is zero in all frequencies.
Such a filter would not be causal, take a look at Kramer-Kronig relations. But for off-line filtering of signals it is possible. More information can be found e.g. here: https://ccrma.stanford.edu/~jos/fp/Zero_Phase_Filters_Even_Impulse.html