The rapid development of data communication in modern era demands secure exchange of information. Steganography is an established method for hiding secret data from an unauthorized access into a cover object in such a way that it is invisible to human eyes. The cover object can be image, text, audio, or video. This paper proposes a secure steganography algorithm that hides a bitstream of the secret text into the least significant bits (LSBs) of the approximation coefficients of the integer wavelet transform (IWT) of grayscale images as well as each component of color images to form stego-images. The embedding and extracting phases of the proposed steganography algorithms are performed using the MATLAB software. Invisibility, payload capacity, and security in terms of peak signal to noise ratio (PSNR) and robustness are the key challenges to steganography. The statistical distortion between the cover images and the stego-images is measured by using the mean square error (MSE) and the PSNR, while the degree of closeness between them is evaluated using the normalized cross correlation (NCC). The experimental results show that, the proposed algorithms can hide the secret text with a large payload capacity with a high level of security and a higher invisibility. Furthermore, the proposed technique is computationally efficient and better results for both PSNR and NCC are achieved compared with the previous algorithms.