In this paper, a compact Giuseppe Peano, Cantor Set, and Sierpinski Carpet fractals based hybrid fractal antenna (GCSA) is designed and developed for Industrial, Scientific and Medical (ISM) band applications. The proposed GCSA is a hybrid fractal design which is created by fusing Giuseppe Peano, Cantor set, and Sierpinski carpet fractals together. The optimization of the microstrip line feed position is performed by using a Firefly Algorithm (FA). The substrate material employed for proposed GCSA is a low-priced, easily available FR4 epoxy of thickness 1.6 mm. By varying the geometrical dimensions of the radiating patch, a data set of 58 GCSAs is randomly generated for the realization of Artificial Neural Network (ANN) and FA approaches. The designed structure is fabricated, and then measured results are evaluated. The proposed GCSA is capable of resonating at 2.4450 GHz with S(1, 1) < −10 dB. The measured bandwidth of the operating ISM band is 101 MHz. The quantitative performance of three different ANN types reveals that Feed Forward Back Propagation ANN (FFBPN) shows minimum error in comparison to other two ANN types. The simulated, experimental, and optimized results show a good match that specifies the preciseness of the measurement.