In this paper, the planar dual-band monopole antenna is presented for Long Term Evolution (LTE) and Wireless Local Area Network (WLAN) applications. The design of the proposed antenna is based on Peano fractal curve and meander line structures. The antenna operates in 1.71 GHz to 2.01 GHz in the desired LTE frequency band and 5.0 GHz to 5.5GHz band (IEEE 802.11a band). The frequency band 1.71 - 2.01 GHz is already available as a study of the current plan according to UMTS and LTE systems (the band no.4). The antenna has been fixed on a substrate boardArlon with εr= 2.33 and thickness of 0.9 mm. Simulation results shows that the proposed antenna has promising radiation characteristics and a reasonable gain of 2.155 dBi at the lower band and 4.772 dBi at the upper band. The simulation and evaluation of antenna performance werecarried out using Microwave Studio Suite of Computer Simulation Technology CST.