Ultrasonic guided wave has received significant attention in the field of nondestructive testing because of their advantages in detecting the entire wall thickness. Since pipe elbows are an important component of the piping system, it is desirable to study the propagation behavior of the guided wave in the elbows. In this paper, instead of using the traditional method of a ring of transducers to generate guided wave at the same time, the propagation behavior of the guided wave in the elbows under the action of a single excitation source is simulated. Using the chirp excitation signal, the transmission signals of the guided wave at different excitation central frequencies are extracted with high efficiency, and the behavior of the guided wave in the elbow under different excitation frequencies is studied. In addition, it is proposed to use the flight time quantity to characterize the complete information of the structure, and the influence of the defects on the flight time is also studied. The results prove that the flight time feature has good detection sensitivity to the defects with varying depth in different locations of the elbow.