Low-voltage fast switchable 1D and 2D Fibonacci grating (FbG), using an electrically suppressed helix ferroelectric liquid crystal (ESHFLC), with high diffraction efficiency for a super-resolution imaging system in far-field are disclosed in this paper. Specifically, the polarization-independent two-domain (0, π) structure is well designed based on photoalignment technology to maximize the total diffraction efficiency that can reach 97.4% (1st order:8.5%, 2nd order: 30%). Apart from that, the FLC gratings offer two tunable states: non-diffractive and diffractive states. Derived from the fast-response property of ferroelectric liquid crystal material, the switching speed of the 1D and 2D ESHFLC-FbG is 103µs at 4 V of the driving voltage. Furthermore, this system achieves the high-resolving power of (λ/2.25) for object detection based upon the intensity map received behind 1D ESHFLC-FbG at far-field. Contribution from the quasi-periodic FbG's special ability to translate the super-resolution information (including at evanescent wave) into the detectable far-field region. Concisely, the proposed ESHFLC-FbG can be a promising candidate for a super-resolution imaging system, superstructure fibre sensor, and other photonic applications.