Sea clutter has a serious influence on the detection performance of a shipborne high‐frequency surface wave radar (HFSWR) system, especially when the target is submerged in the spread Doppler spectrum of the first‐order sea clutter. A prediction cancellation (PC) method based on the radial basis function neural network (RBFNN) is put forward to suppress the first‐order sea clutter in time domain for shipborne HFSWR. Using the RBFNN trained by the averaged sea clutter data from the range cells surrounding the range cell of interest, the PC algorithm is implemented in the interested range cell. Compared with the two‐dimensional fast Fourier transformation plus digital beam forming algorithm, the proposed PC algorithm is shown to give far superior sea clutter suppression results based on real data.