A new type of dual-wideband bandpass filter using composite series and shunt resonators is proposed in conjunction with its direct synthesis and design theory. By making use of the transmission pole (TP) and the transmission zero of the composite resonators flexibly, a dual-wideband filter with a wide range of frequency and bandwidth ratios as well as a wide stopband can be realised. With a shunt capacitor introduced at each I/O port, extra TPs either in the low passband or in the high passband can be created, leading to more filter design options. To give a direct design procedure, a lumped-element prototype is first synthesised based on a target filtering function and a dedicated circuit extraction process. The filter layout can be realised using semi-distributed circuits and chip capacitors. Two practical schemes are introduced to suppress spurious resonances for a wide high-rejection stopband. Two filter examples are designed with a small and a large frequency ratio and a wide band suppressed spurious resonances. The unique filter response and good agreement between the designed and measured results demonstrate the superior performance of the proposed filter structure and the effectiveness of the synthesis and design theory.