In the application of tumor ablation with pulsed electric field, bipolar pulses can ablate tumors more homogeneously than unipolar pulses. However, it is difficult to generate bipolar high voltage nanosecond or sub-microsecond pulses due to the strong electromagnetic interference and strict requirements of control precision. In this paper, a bipolar Solid-State Linear Transformer Driver (SSLTD) is designed. The SSLTD is composed of many LTD modules with the same structure and their secondary windings are reversely connected in series to generate bipolar narrow pulses over the load. To generate stable pulses, the reset of the pulsed transformers is the key technique in bipolar SSLTD. Through the resistive load experiments, the influence of the forms of reset current on the reset effect is compared and analyzed, and the influence of the voltage amplitude, pulse width, interval between positive and negative pulses, the number of parallel switches in each module, and the reset current amplitude on the output pulses is analyzed. Experimental results show that the designed bipolar SSLTD can generate repetitive bipolar nanosecond pulses with voltage amplitude up to 5 kV, adjustable pulse widths of 80-400 ns, the rising and falling 20-50 ns over 500 Ω load. Besides, reverse series DC reset circuit which is simple in structure has a better reset effect than pulsed reset circuit. The bipolar SSLTD can generate nanosecond pulses with any polarity and has many advantages such as compact size, modularity, low electric stress.