Stepped frequency ground penetrating radar (SFGPR) has received increasing attention in the field of ground penetrating radar technology due to its superiority in the detection performance. Compressed sensing (CS) SFGPR imaging reconstruction method can not merely reduce the measured imaging data volume, but also reconstruct target image with less sidelobe. However, the imaging algorithm using CS approach will lose efficacy in strong clutter environment. To solve this problem, a CS SFGPR imaging reconstruction method combined with subspace projection clutter suppression approach is proposed in this paper. First, all frequency domain data at each measurement position are reconstructed from reduced frequency measurements via sparse reconstruction technique. Then subspace projection ground clutter suppression technique is used to suppress the strong ground clutter. Finally, the orthogonal matching pursuit (OMP) algorithm is utilized to reconstruct the underground target image. Synthetic and experimental data processing results have verified the effectiveness and accuracy of the proposed imaging method.