With a focus on the coupling problems of multivariable control for the paper cross-directional (CD) basis weight caused by a hydraulic headbox, a novel approach of multivariable decoupling control based on sparse decomposition is proposed. The model function of the CD basis weight control for a single dilution water branch valve is used as the basis of a sparse atomic library. Then, according to the deviation curve of the CD basis weight, the particle swarm optimization (PSO) algorithm is used to obtain atoms corresponding to each control unit (the multiple dilution water branch valves) to form a sparse atomic library. As each atom in the atomic library contains the control information of the corresponding dilution water branch valve, the decoupling control of paper CD basis weight can be realized via mining control information. The essence of this method is to solve the coupling problems of multivariable control by using optimization theory. Experimental results demonstrate that this method achieves a remarkable decoupling control effect.