A linearized mathematical model for the pressurized water reactor (PWR) core dynamics is presented based on conservation of energy and mass balance. The core and coolant system are treated as a lumped parameter while considering the delayed neutron effect. The developed model is controlled by negative feedback reactivity from the coefficients of reactivity in the fuel and reactor coolant. The model state variables are linearized first order differential equations with a steady state initial value and put in state space using Matlab/Simulink. The reactor core dynamic response is investigated through transients introduced to the core model inlets represented in external reactivity insertion eg. (0.001 Δk/k), 10% step decrease in core flow rate and 10 oF step decrease in core inlet coolant temperature. The simulation results demonstrated the role of feedback reactivity form coolant temperature and Doppler Effect in stabilizing the core power and affecting the steady state values of core variables.