We conducted numerical simulations of heat conduction in one-dimensional (1D) nonlinear lattices to reveal the mechanism of thermal rectification of asymmetrically-defective materials. A decreased spring constant simulates the defective lattice and the obtained temperature profile suggests a thermal resistance existing at the interface of two linked segments with different spring constants. Our numerical results suggest that the thermal rectification of two-segment system is dependent on the spring constant and temperature gradient. Introducing the estimated phonon band, most of the rectification mechanisms are clearly explained and performance limit as a thermal rectifier is found for the defective/pristine materials.