In this study, a direct synthesis approach is proposed to extract the coupling matrix of multi-port filtering power divider (FPD) with arbitrary phase shift, power division as well as reference impedances, for the first time. This method provides an attractive technique to synthesise a multi-functional device that combines the characteristics of bandpass filter, multi-port power divider and ideal phase shifters as well as the impedance matching network, which can effectively diminish the overall size and improve the performance of the microwave front-end network. A newly defined coupling matrix corresponding to arbitrary multi-port topologies that introduces ideal phase shift by virtue of constant frequency-independent reactance at the source and load is developed in FPD synthesis process. The coupling matrix is obtained directly by optimising the presented cost-function in this paper, avoiding complex similar transformation process of coupling matrix. Finally, several numerical examples of multi-port FPD with equal/unequal power division ratio, arbitrary phase shift and reference impedances are synthesised to well verify the proposed synthesis method, and a practical example is given to verify the validity of arbitrary phase shift and arbitrary reference impedance.