A high-gain, dual-band Double-Material Substrate (DMS) Cylindrical Surrounding micro-strip fed Patch Antenna (CSPA) composed of FR-4 (lossy), polyimide (lossy), and a partial ground plane of copper (annealed) have been proposed. In addition, it has been presented for use in IEEE 802.11, Wireless Local Area Network (WLAN) standards of 2.4 GHz (2.4 GHz ~ 2.484 GHz), 5.2 GHz (5.15 GHz ~ 5.35 GHz), and 5.8 GHz (5.725 GHz ~ 5.825 GHz), IEEE 802.16 Worldwide Interoperability for Microwave Access (WiMAX) standards of 2.5 GHz (2.5 GHz ~ 2.69 GHz) and 5.2 GHz (5.2 GHz ~ 5.8 GHz) and middle band of 5 G technology (2.3 GHz ~ 2.4 GHz and 2.5 ~ 2.69 GHz). The proposed antenna is a solution to the negative effect of dimension inaccuracy resulting from high permittivity substrate material used for CSPA design at high frequency. The antenna has been designed, simulated, and extensively analyzed for operation at frequencies ranging from 2.28 GHz ~ 3 GHz and 4.9 GHz ~ 6.1 GHz, providing an impedance bandwidth of 0.7 GHz and 1.1 GHz at the resonance frequency of 2.68 GHz and 5.5 GHz, respectively. In addition, by varying specific antenna dimensions at 5.5 GHz, the DMS CSPA has been observed to produce a Voltage Standing Wave Ratio (VSWR), directivity, gain, and radiation efficiency of 1.13, 8.19 dBi, 6.573 dBi, and 81 %, respectively.