Hydrogen Peroxide monopropellant thruster has advantages of utilizing environmentally-friendly green propellant and has high reliability due to system simplicity. It has been used in applications such as the attitude control system of launch vehicles or the descent engines of the lander spacecraft. The major failure modes of the monopropellant thrusters are induced by the phenomena occurring during the transient period; 1) fail to achieve steady-state condition at the ignition transient, 2) combustion instability during the steady-state operation. In the current work, a novel dynamic model was developed to emulate the ignition transient of the catalytic reactor and improved the existing concentrated combustion model to predict the occurrence of the combustion instability during the steady-state operation. Comparison with the experimental data from the firing tests was conducted for the validation, and the models were utilized in predicting the changes of the thruster responses according to the design configurations and operating conditions. Also, a preliminary design method for stable operation of the monopropellant thruster was suggested using the results from the parametric studies.