We concentrate on describing the important influence and physical law of the split resonant ring (SRR) based left-handed materials on patch antennae. The finite-difference time-domain method, together with the finite element method is used to study the characteristics of patch antennae based on composite rectangular SRRs. A novel composite rectangular SRR system is formed by assembling the conventional patch antennae and SRRs, it is found that electromagnetic wave resonance occurs near f=3.15GHz, the equivalent permittivity and permeability are both negative, and the electromagnetic wave’s tunnel effect and evanescent waves’ enhancing effect are formed, which can improve the localization extent of electromagnetic wave’s energy apparently. Such effects can improve the antenna’s radiation gain and its matching condition. The phenomenon indicates that such composite rectangular patch antennae are promising in wireless communications such as mobile phones, satellite communication and aviation.