Traditional Mathematical Morphology (TMM) is not well in structure-preserving, and the existing adaptive modified methods usually miss mathematical properties. To address the problems, a Guided Adaptive Mathematical Morphology (GAMM) for multimodal images was proposed. Firstly, the structure elements were constructed by considering the joint information of the input and the guidance images, so that the corresponding operators were more robust to the noise. Secondly, according to 3σ rule, the selected members of structure elements were able to be adapted to image contents. Finally, by using the Hadamard product of sparse matrices, the structure elements were imposed with a symmetry constraint. Both of the theoretical verification and simulation show that the corresponding operators of the proposed mathematical morphology can have important mathematical properties, such as order preservation and adjunction, at the same time. Denoising experimental results on multimodal images show that the Peak Signal-to-Noise Ratio (PSNR) of GAMM is 2 to 3 dB higher than those of TMM and Robust Adaptive Mathematical Morphology (RAMM). Meanwhile, comparison of subjective visual effect shows that GAMM significantly outperforms TMM and RAMM in noise removal and structure preservation.