A tree-type nanoporous filtering membrane with complex pores is proposed. The membrane consists of three kinds of concentric cylindrical pores across the membrane thickness i.e. the four branch pores for filtration, the one flow-collecting pore and the one flow resistance-reducing pore. The ratio of the radius of the flow resistance-reducing pore to that of the filtration pore is optimized for yielding the highest flux of the membrane. The dimensionless lowest flow resistance of the membrane in the optimum condition was typically calculated for different filtration pore radii and different passing liquid-pore wall interactions. The capability of the membrane for a liquid-liquid separation was also investigated. It was found that the proposed membrane has improved manufacturing properties without loss of the mechanical strength, the high flux and the liquid-particle or liquid-liquid separation capabilities.