This paper presents a new realization structure for Goertzel algorithm which utilizes the hardware architecture of many kinds of signal processors（i.e.DSP）.And actual test indicates that the efficiency of the new realization structure has improved 3.7 times than the original realization structure.The recursion step of Goertzel algorithm can be regarded as an AR（2） process and generalization of the improved realization structure to AR（p） process has been considered in this paper.A resolution for hardware implementation on the PLD（i.e.FPGA） of the improved realization structure for Goertzel algorithm has been proposed.