Steganography is the process of concealing sensitive information within cover medium. This study offers an efficient and safe innovative image steganography approach based on graph signal processing (GSP). To scramble the secret image, Arnold cat map transform is used, then Spectral graph wavelet is used to change the cover and scrambled secret image, followed by singular vector decomposition (SVD) of the modified cover image. To create the stego image, an alpha blending process is used. To produce the stego image, GSP-based synthesis is used. By maintaining the inter-pixel correlation, GSP improves the visual quality of the produced stego image. The effects of image processing attacks on the suggested approach are examined. The investigational results and assessment indicate that the proposed steganography scheme is more efficient and robust in terms of quality measures. The quality of stego image is evaluated in respect of PSNR, NCC, SC and AD performance metrics.