This study presents a novel dual-band filtering power divider (DB-FPD) structure with independently controllable bandwidths for dual-band application. The proposed DB-FPD structure is constructed by shorted G- and T-shaped patch resonators, and meandered slot lines are etched on shorted patch resonators to generate resonance in the upper band. The 3 dB fractional bandwidth (FBW) of designed DB-FPD structure in a lower band (upper band) can be adjusted from 5.2 to 24.2% (3.1 to 26.9%), respectively, using a substrate of 31 mil thick TLY-5. The even-/odd-mode method is adopted to demonstrate the power splitting and isolation performances. The lumped-element equivalent circuit is extracted to explain the power splitting transmission performance. Also, the coupling matrix analysis is applied to present the detailed design procedures for practical DB-FPD, with specific passband bandwidths and centre frequencies of dual passbands. Finally, the isolation performances are analysed with different isolation resistor values and loading positions. For verification, two DB-FPDs with equal absolute bandwidths (ABW) and equal FBWs are simulated, fabricated and measured for dual-band WLAN application. The measured results agree well with the simulated ones, exhibiting a favourable frequency selectivity and controllable passband bandwidths.