We propose a polarization-filtering and polarization-maintaining negative curvature fiber in which two nested resonant tubes are added to a standard negative curvature fiber with one ring of tubes. The coupling between the glass modes in the nested resonant tubes and the fundamental core modes is used to increase the birefringence and differential loss for the fundamental core modes in the two polarizations. We show computationally that the birefringence and the loss ratio between the modes in the two polarizations can reach 10 and 850, respectively. Meanwhile, the low-loss mode has a loss that is lower than 0.02 dB/m. The relatively simple design of this polarization-maintaining negative curvature fiber will be useful in hollow-core fiber devices that are sensitive to polarization effects, such as fiber lasers, fiber interferometers, and fiber sensors.