In skywave over-the-horizon radar (OTHR), transient interference is always suppressed with steps of interference localisation, corruption segment blanking and data restoration. The gapped data amplitude and phase estimation (GAPES) method has been proved to achieve good restoration performance. However, the large computational cost limits its application. A computationally efficient method for transient interference suppression is proposed. Quadratic smoothing is used to suppress transient interference instead of blanking the contaminated data. After that, the GAPES method only needs to restore the smoothed target echoes. Since quadratic smoothing can preserve most clutter echoes, the GAPES method will converge much faster. Experimental results demonstrated the effectiveness of the proposed method.