Dual-band microstrip antenna is designed for industrial-scientific-medical(ISM) band of 2.4㎓ and 5.8㎓ using finite-difference time-domain method(FDTD). Cross Patch fed 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 by aperture and stub length change is examined. And it is investigated that center frequency and -10 ㏈ bandwidth by Length of radiation element and width change. Experimental result about reflection Loss confirmed that agree well with analysis results of FDTD and IE3D, And -3 ㏈ beam width, front to back ratio and gain in frequency 2.43㎓ and 5.79㎓ is presented by measuring radiation Pattern of antenna.