Maintaining high fundamental mode purity in low‐loss single‐ring hollow‐core photonic crystal fiber remains a key challenge. Here a double‐clad anti‐resonant‐reflecting design is reported that, through modal filtering, provides high suppression of higher‐order modes while maintaining a low‐loss fundamental mode. The structure consists of a ring of six thin‐walled capillaries fused to the inner wall of a thicker‐walled capillary that is in turn fused at a single point to the silica outer cladding. Greater than 40 dB m−1 suppression of higher order modes over a 6 nm wide window whose central wavelength can be tuned by adjusting the gas pressure is observed. The novel design paves the way to practical applications of such fibers in high‐quality laser beam delivery and low‐noise optical‐signal transmission. [ABSTRACT FROM AUTHOR]