Given a space of homogeneous type (X,μ,d), we prove strong-type weighted norm inequalities for the Hardy-Littlewood maximal operator over the variable exponent Lebesgue spaces L\pp. We prove that the variable Muckenhoupt condition \App is necessary and sufficient for the strong type inequality if \pp satisfies log-H"older continuity conditions and 1<p−≤p+<∞. Our results generalize to spaces of homogeneous type the analogous results in Euclidean space proved in [14].