Carbon nanotubes (CNT) are robust and proven as promising building blocks for oil/water separating membranes. However, according to classic fluid dynamic theory, achieving high permeation flux without sacrificing other membrane properties is a formidable challenge for CNT membranes, because of the trade-off nature among key membrane parameters. Herein, to relieve the trade-off between permeation fluxes, oil rejection rate, and membrane thickness, we present a new concept to engineer CNT membranes with a three-dimensional (3D) architecture. Apart from achieving high oil separation efficiency (>99.9%), these new oil/water separating membranes can achieve water flux as high as 5,500 L/m2.h.bar, which is one order of magnitude higher than pristine CNT membranes. Most importantly, these outstanding properties can be achieved without drastically slashing membrane thickness down to nanoscale. The present study sheds a new light for the adoption of CNT-based membranes in oil/water separation industry.