The chemisorption of a 12-hydroxydodecanoic acid (HDA) molecule on the Si(001)-(2 x 2) surface is investigated by first principles density-functional calculations within the generalized gradient approximation. We assume two different orientations of this molecule on the hydroxylated surface: (i) a linear and (ii) an angular situation on the above pedestal position. Within each orientations, we consider two different end groups of the molecule on the surface, i.e., hydroxyl and carboxylic acid group. Upon their relaxations, the linear bonding model with hydroxyl end group of HDA molecule on the hydroxylated Si(001) surface is found to be more energetically favorable than the other cases by 0.34 eV per HDA molecule. The band structure and the surface charge densities are also analyzed for this system. It is observed that the chemisorption of HDA has considerably affected the surface electronic structure of the clean Si(001)-(2 x 2) surface.