Hydrogen adsorption dissociation on clusters is a widely studied subject that provides the opportunity to gain a basic understanding of the complicated nature of many interesting problems, such as hydrogen embrittlement of metals, catalytic processes, hydrogen storage, etc. In this study, I present density functional calculations of H-2 adsorption and dissociation on small-sized AlnCr clusters for n = 1-13. My results show that H-2 is easily physically absorbed on the top Cr atom of AlnCr clusters with a side-on orientation rather than an end-on orientation. In addition, I investigate a possible dissociation mechanism and dissociation pathway of H-2 on selected Al2Cr and Al7Cr. My findings suggest that the hydrogen dissociation behavior on AlnCr clusters characterized by the activation barrier and reaction energy can be tuned by controllable doping. Thus, Al2Cr and Al7Cr clusters might serve as highly efficient and low-cost catalysts for hydrogen dissociation.