This paper presents a new chaos-based image encryption method using a hybrid effect of bit-level and pixel-level image encryption principles to form an encrypted digital image. In the proposed encryption scheme, the 2D logistic map generates two pseudo-random chaotic streams that are employed in an efficacious way to use the bit-level and pixel-level ideologies to encrypt the plain image. The two chaotic sequences produced by the 2D logistic map are used to create two LSB-based bit-matrices to form a bit-level perspective that helps in the scrambling of the image. Furthermore, the same two chaotic streams of the 2D logistic map are used in a cross manner at the pixel level to diffuse the image and finally form a strong cipher image. The experimental numerical results, standard reference value tests, and comparative analysis with the existing encryption methods support and validate the reliability and robustness of the proposed encryption approach.