In this work, a multiband log-periodic dipole array (LPDA) antenna, which can operate between 0.5 GHz and 4 GHz, is designed for microwave imaging applications. Design includes two steps. In the first step, LPDA antenna design is achieved by means of several simulations. In the next step, the lengths of each dipole is reduced to obtain a smaller antenna. For this purpose, each dipole is shortened with the microstrip lines, which are printed on the back of the antenna. In the design process, specific reflection coefficient, VSWR, gain and radition pattern are considered as the main goals. Designed antenna is printed on a FR4 substrate and simulation results are compared with the measured data.