This paper presents a generalized predictive control (GPC) strategy for a spatially distributed transport-reaction process based on time space decomposition. First, the Karhunen-Loeve (K-L) decomposition is used for time space decomposition to find the principal spatial structures and to reduce the dimension of the data. Then, an autoregressive exogenous (ARX) model is identified using the excitation input signals and the temporal coefficients obtained by the K-L decomposition. A GPC strategy is investigated based on the ARX model, with or without considering the system constraints. Numerical simulations on a catalytic rod illustrate the effectiveness of the proposed methods.