A Linear Matrix Inequality (LMI) approach for designing the H-infinity Proportional-Integral (PI) controller for a nonlinear dynamic system is studied. A local linear model containing time-varying norm-bounded uncertain parameters is identified at first. The robust PI control design problem based on the norm-bounded uncertain linear model is then transformed into a standard H-infinity control problem, where the latter is further formulated as LMIs. By adopting the LMI expression, a symmetric positive definite matrix P with guaranteed overall system's quadratic stability can be easily determined. The matrix P can finally be used to infer the robust PI controller parameters. One chemical process, a non-isothermal continuous-stirred-tank reactor (CSTR) with a first-order exothermic reaction, is illustrated to demonstrate the effectiveness of the proposed LMI-based H-infinity PI controller design method for nonlinear dynamic processes.