This paper presents a model predictive control approach using the Koopman operator for tracking concentration and temperature in continuous stirred tank reactor(CSTR) systems. A 24-dimensional Koopman-based linear model serves as the predictive model. The method combines predictive control with receding horizon multi-objective optimization, considering state constraints and control objectives. Matlab/Simulink simulations validate its effectiveness, and comparisons with local linear model predictive control(LMPC) and nonlinear model predictive control(NMPC) algorithms demonstrate faster convergence and higher control accuracy without requiring precise system models or solving non-convex optimizations.