Antireflection coatings are vital for reducing loss due to optical reflection in photovoltaic solar cells. A single-layer magnesium fluoride (MgF2) antireflection coating is usually used in thinfilm CIGS solar cells. According to optics, this coating can be effective only for a narrow spectral regime. Further reduction of reflection loss may require an optimal single-layer or multi-layer coating. Hence, we optimized the refractive indices and thicknesses of single- and double-layer antireflection coatings for CIGS solar cells containing a CIGS absorber layer with: (i) homogeneous bandgap, (ii) linearly graded bandgap, or (iii) nonlinearly graded bandgap. A relative enhancement of up to 1.83% is predicted with an optimal double-layer antireflection coating compared to the efficiency with a single-layer antireflection coating.