Feeding network with complex weight has important prospect in various applications. In this article, the design of complex weighted feeding network based on generalized coupled-resonator filter theory is proposed. To design the power and phase distribution all-in-one, a novel type of multifunctional generalized filter is proposed. It has abilities of impedance transformation, phase shift, and filtering. Then, the design method of the network with arbitrary power distribution and arbitrary phase distribution by this generalized filter is demonstrated. Four different design examples are executed to validate the proposed theory. This proposed network overcomes many shortages of these existing methods and possesses several additional advantages, such as simple structure, designable bandwidth, and filtering function.