This article concerns an inverse problem for a strongly coupled reaction-diffusion system, which has many applications including the cross diffusion resulted from the influence of one component on another. This inverse problem aims to determine a spatially varying coefficient in the reaction-diffusion system from internal observation data on an arbitrary subdomain. We use a new Carleman estimate to derive Hölder stability for this inverse problem. Different from the existing methods dealing with weakly or strongly coupled system, such as Fan & Chen (2012, Stability estimates for a strongly coupled parabolic system. Tamkang J. Math., 43, 137–144.) and Bellassoued & Yamamoto (2013, Carleman estimate and inverse source problem for Biot’s equations describing wave propagation in porous media. Inverse Probl., 29, 115002 (20pp).), we consider the two equations governing the strongly coupled system as a whole to establish the needed Carleman estimate, assuming only that the determinant of coefficient matrix of principle terms is not zero.