A time-space steerable point-focusing Frequency Diverse Array (FDA) antenna based on multi-carrier frequency with time-modulated frequency offset is proposed.In order to achieve the tracking of the moving target, a time compensation factor is introduced in the frequency offset to avoid the possible frequency singularity, so that the duration of the continuous frequency modulation is much longer than that of the periodic modulation.Then the frequency offset is calculated according to the real-time position of the target to achieve the goal of keeping the beam focused on the target throughout the whole process of itsmotion. Finally, a simulation example of moving target tracking is given to verify the effectiveness of the method.