We report on the design of an all-dielectric quasiperiodic grating coupler with rectangular Si ribs on a SiO₂ substrate. The structure consists of ten periods built by alternating Si ribs and air according to the S₄ step of the Fibonacci series, i.e., the period was made as <i>ABAAB</i>, where <i>A (B)</i> can be used as Si (air) or air (Si). The thicknesses of air and Si ribs were taken as 315 nm, with a total length for the unit cell of 1575 nm. The finite- difference time-domain (FDTD) technique was used to obtain the numerical data within the commercial software Lumerical FDTD. Multiple coupling efficiency peaks were observed owing to self-similarity effects. Furthermore, we show numerically that optimum wavelengths and coupling efficiency amplitudes can be tailored by varying the ribs' etch-depth and the angle of incidence from the optical fiber, which makes the proposal relevant for efficient, broadband optoelectronic circuits.