�This paper describes the synthesis of a bandpass filter to achieve high selectivity and rejection properties using a new class of filter functions called chained-elliptic function filters. Chained-elliptic filters have higher selectivity than Chebyshev function filters and have the property of sensitivity to manufacturing tolerance reduction in chained-function filters. The proposed design has high selectivity and reduced sensitivity, enabling easier and faster filter fabrication. The characteristic polynomials of chained-elliptic function filters are derived (through chaining elliptic filtering function) and extracted to form a coupling matrix of the bandpass filter. The novel transfer polynomials are given in detail, and a thorough investigation of the filter characteristics is performed. A theoretical comparison with Chebyshev and elliptic filters of the same order is performed to ascertain the demonstrated advantages of this proposed filter class. A high frequency narrow-band fourth-order chained-elliptic function waveguide filter centred at 28 GHz with a fractional bandwidth of 1.61 is fabricated to validate the proposed design concept. A good match among the measured, simulated, and ideal filter responses is shown where the overall responses between measurement and simulation have a difference of approximately 2 which is within the acceptable limit. The chained-elliptic function concept will be useful in designing low-cost high-performance microwave filters with various fabrication technologies for millimetre-wave applications. © 2020, Electromagnetics Academy. All rights reserved.