Electromagnetic multipoles enable rich electromagnetic interactions in a metasurface and offer another degree of freedom to control electromagnetic responses. In this work, we design and experimentally demonstrate an optically transparent, flexible and broadband microwave metasurface absorber based on multipolar interference engineering. Different from previous works, the designed metasurface simultaneously supports fundamental electric dipole and high-order electric quadrupole mode, whose interference satisfies the back-scattering suppression condition based on the generalized Kerker effect and thus high absorption. The measurement results indicate that the fabricated metasurface exhibits a high average absorption of 89% in the microwave band from 4 GHz to 18 GHz, together with a good optical transparency. Our study offers an alternative approach for designing broadband microwave metasurface absorber, which is potentially applicable in electromagnetic shielding, radar stealth and energy harvesting.