Most recently, polydopamine (PDA) and its hybrid nanomaterials have been developed as promising adsorbents to remove organic dyes. However, PDA based adsorbents are typically lack of recyclability, alkali resistant and selective adsorption. Herein, novel PDA based magnetic nanoparticles are fabricated for the first time via the simultaneous incorporation of PDA and poly(ethylenimine) (PEI) on Fe3O4 nanoparticles simply in one step to overcome almost all disadvantages of "traditional" PDA adsorbents. The constructed PDA based magnetic nanoparticles have ultrathin shell layer (only about 3 nm, much thinner than that of other PDA adsorbents), and can withstand strong alkaline solutions (0.1 M NaOH, pH=13), exhibiting excellent alkali resistance. Remarkably, the nanoparticles show superior performance in smart and fast selective removal (>95%, just in five minutes) of anionic dyes from dye mixtures and can maintain their high efficiency (>90%) even after 10 cycles, indicating the unprecedented selective adsorption capacity and desirable recyclability. The adsorption process follows pseudo-second order reaction kinetics, as well as Langmuir isotherm, indicating that anionic dyes are monolayer adsorbed on the hybrid by electrostatic interaction. In particular, the readily regeneration of the novel composite nanoparticles can be accomplished only within several minutes, demonstrating excellent regeneration ability. Our work can provide new insights into utilizing mussel-inspired materials for environmental remediation and creating advanced magnetic materials for various promising applications.