The paper analyses the characteristics of radio frequency interference (RFI) in HF surface wave radar (HFSWR) which adopts the linear frequency modulated interrupted continuous wave (FMICW). RFI will influence all the range cells including all the positive frequency and negative frequency, and the negative frequency range cells contain only the interference information. Based on the above characteristics, we introduce and analyze a new adaptive interference mitigation beamforming algorithm using the negative frequency range cells samples to estimate the interference covariance matrix. Experimental results confirm that this general and robust algorithm can achieve effective RFI suppression using the data recorded by the HFSWR, located near Zhoushan in Zhejiang China. The paper analyzes the characteristics of radio frequency interference (RFI) in HF surface wave radar (HFSWR) which takes the linear frequency modulated interrupted continuous wave (FMICW). RFI will influence all the range cells including all the positive frequency and negative frequency, and the negative frequency range cells contain only the interference information. Based on the above characteristics, we introduce and analyze a new adaptive interference mitigation beamforming algorithm using the negative frequency range cells samples to estimate the interference covariance matrix. Experimental results confirm that this general and robust algorithm can achieve effective RFI suppression using the data recorded by the HFSWR, located near Zhoushan in Zhejiang China.