According to compressive sensing theory, a compressive sensing based normalized ghost imaging method was proposed. Firstly, the measurements of a bucket detector were normalized, and the measurement matrix was constructed with speckle fields.Then, the object image was reconstructed with a low number of measurements by adopting orthogonal matching pursuit method. Several experiments were performed by using gray-scale images and binary images respectively as the imaging targets and the Peak Signal to Noise Ratio(PSNR) as the yardstick. The reconstruction effects were quantized and compared for traditional Ghost Imaging(GI), Normalized Ghost Imaging(NGI) and Compressive Sensing based Normalized Ghost Imaging(CSNGI) respectively. The simulation results indicate that the PSNR of CSNGI is about 6 dB and 2 dB higher than those of GI and NGI on gray-scale images with more details, and 3.4-4.3 dB and 5.2-6.5 dB higher than those of NGI and GI for binary images with less details, respectively. Finally, the actual speckle field measured by Charge Coupled Devices(CCDs) was used to construct the measurement matrix, and the experiment results also further indicate that the CSNGI improves the reconstruction quality greatly.