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Distributed parameter systems (DPS) widely exist in the large-scale industrial production industry. Techniques developed for DPS can further demonstrate the complexity of the industrial process, such as the hot-rolled strip laminar cooling (HSLC) process. Due to the infinite dimensional of states variables and manipulated variables, it is a challenging work to model and monitor for DPS in practice. In this paper, a data-driven approach for process modeling and quality monitoring of DPS is obtained. A second-order partial differential equation (PDE) is transformed into finite-dimensional model of ordinary differential equation (ODE) with finite element method (FEM) and Galerkin method. Then, this model is described by state space with time-space separation. To realize the proposed scheme by the data-driven approach, we use the industrial process data to estimate the parameters in the model and basic functions by recursive least squares method. Based on this model, a kernel representation of DPS for residual generation is obtained in the statistical framework. <inline-formula> <tex-math notation="LaTeX">$T^{2}$ </tex-math></inline-formula> statistic is employed to evaluate the residual and the threshold is determined by the use of noncentral <inline-formula> <tex-math notation="LaTeX">$\chi ^{2}$ </tex-math></inline-formula>-distribution. Finally, the effectiveness of the proposed scheme is demonstrated by conducting a simulation on the production process of HSLC.