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 (LMPC) and nonlinear (NMPC) algorithms demonstrate faster convergence and higher control accuracy without requiring precise system models or solving non-convex optimizations.