In this paper, a stepped-frequency radar with frequency range from 0.8 GHz to 4 GHz is proposed to 'scan' the ground using a relatively long antenna array. This 1D array has a very narrow beam-width along the movement direction but a wide beam-width along the array axis, thus the radar can efficiently detect buried objects with reasonable accuracy and the algorithm for data interpretation can also be relatively simple and straightforward. Because of its excellent wideband performance, the tapered slot antenna is chosen as the array element for the system. The focus of our study is on the optimum design and performance evaluation of the antenna array. The optimizations of the element antenna, the spacing of elements, the length of the array and the arrangement of the transmitting and receiving arrays are investigated by means of analytical and numerical (finite-different time- domain) simulations. Both the near and far fields of the array are obtained in the time and frequency domains. The signal returns from some typical objects (such as a pipe and a land- mine) are also investigated. It's demonstrated that the proposed TSA array system is viable for efficient and accurate detection of subsurface objects.