Dual-band microstrip antenna is designed for industrial-scientific-medical(ISM) band of 2.4 GHz and 5.8 GHz using finite-difference time-domain method(FDTD). Cross patch 130 by aperture in the ground plane of microstrip line is proposed as radiation element of antenna which is 2 rectangular patch is overlapped. To design antenna, change of input impedance is examined by length change of aperture and stub. And center frequency and - 10 dB bandwidth are investigated by change of length and width in radiation element. Measured result about reflection loss confirm that agree well with simulation results of FDTD and IE3D. And 3 dB beam width, front to back ratio and maximum gain is presented by measuring radiation pattern of antenna in frequency 2.43 GHz and 5.79 GHz.