Laser beam steering or pointing, which stabilizes the beam direction, is critical in many areas, such as optical communication systems, astronomy and directed-energy systems etc. However, the disturbances including atmospheric turbulence and mechanical jitter on platform may degrade the pointing accuracy. A proportional-integral (PI) feedback control commonly has been used in the track loop with a fast steering mirror. To compensate dynamic disturbance effectively, the laser beam steering control system must have a larger bandwidth than the disturbance bandwidth. But the control bandwidth is limited by the noise of the sensor, computing latency, and the light energy. So, a simple proportional-integral (PI) feedback controller of a piezoelectric fast steering mirror (PFSM) can only compensate the broadband disturbance of the atmospheric turbulence, but cannot effectively compensate a larger amplitude narrowband jitter because of the low control bandwidth. Moreover, when the control bandwidth is tuned to high, the mechanical resonance of the PFSM can cause the instability of the system. An improved dual two-order filter assisted high-bandwidth control algorithm to improve the pointing accuracy and error attenuation capability is proposed. This method can control a PFSM for suppression of laser beam jitter. The influence of filter parameters on frequency characteristics is analyzed, and then, a practical design method is proposed. The dual two-order filter can combine the characteristics of traditional notch filter and two-order low-pass filter, and can also obtain any desired amplitude in the interesting frequency ragion with little influence on the others. The principle of the proposed filter for suppressing the mechanical resonance of the PFSM and the narrowband disturbance is elaborated. And then, the different dual two-order filters are designed according to the frequency content of the PFSM and the narrowband disturbance. Finally, the proposed dual two-order filter assisted PI control algorithm and classic PI control algorithm are compared with each other. Experimental results show that, in the same conditions, the pointing accuracy of the proposed two-order filter assisted PI control algorithm is nearly 5 times better than that of the classic PI control algorithm, and the error attenuation bandwidth is one time higher. It also indicates that the proposed algorithm does not need an additional sensor; it is simple and effective for the suppression of the mechanical resonance of a PFSM and that of the narrowband disturbance, hence it improves the system error attenuation bandwidth and the beam pointing accuracy.