This paper presents a new dual band planar fractal antenna based on an elliptic geometry. The antenna results show two resonance frequencies at 2.35 GHz and 5.8 GHz with a -10 dB return loss bandwidths respectively of 750 MHz and 320 MHz which cover Universal Mobile Telecommunications System band (1920 - 1980 MHz / 2110 - 2170 MHz) and Industrial, Scientific and Medical bands (2400 - 2500 MHz and 5725 - 5875 MHz). The antenna originality resides in its small size 55 × 30 mm² implemented over an FR4 substrate of 4.4 for relative permittivity, 1.6 mm for thickness and 0.025 for loss tangent.