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A coplanar waveguide fed (CPW-Fed) monopole antenna with dual band-notched characteristics is presented in this paper. The design and simulation of the antenna is completed by High Frequency Structure Simulator (HFSS) software. HFSS is a frequency-domain simulation software based on Finite Element Method (FEM). With the help of this software, the proposed antenna has very good performance. It consists of stepped rectangle patch, stepped ground planes and stepped feed lines. These steps improve the input impedance bandwidth and radiation characteristics. By removing a U-shaped slot and C-shaped one from the stepped patch, band rejected property in the 3.5GHz/5.5GHz band is obtained. Moreover, the two bands can be adjusted independently. The compact antenna has the promising performance including broadband impedance matching, consistent radiation pattern and stable gain.