Based on a stacked array consisted of vertically cascaded four pairs of metal dielectric bilayers, a one-dimensional double-frequency absorber with polarization insensitive and fabrication-tolerant is designed. Simulation results show that the absorber can implement double-frequency polarization insensitive absorption based on the absorption principle of magnetic excitation resonance to TM polarization wave absorption and waveguide mode resonance to TE polarization wave absorption. Structure parameters are predicted through LC equivalent circuit and eigen equation, and the electromagnetic field distribution is analyzed to further understand the absorption principle of the absorber. More importantly, the insensitive structure of the one-dimensional absorber is independent for TM and TE polarization wave absorption, and the absorption characteristics of the absorber is less affected by the spacing distance between the neighboring stacks, which make more free and flexible in the design, make the absorber extremely simple in fabrication and have high flexibility, with covering the range of electromagnetic waves from microwave frequencies extended to terahertz. The research on the absorber is very important to the absorber development and it will have better application prospect.