Ultrasonic wave velocity is an important manifestation of coal elastic properties and is extremely useful for coal and coalbed methane exploration. In this study, we focused on analyzing how the molecular structure affects the elastic ultrasonic wave velocity. High-resolution transmission electron microscopy (HRTEM) and Fourier transform infrared spectroscopy (FT-IR) were used to explain the coal’s molecular structure. Ultrasonic wave velocity measurements were then used to determine the elastic parameters of coals of different ranks. From an elasticity theory point of view, the molecular structure of coal is a simple system consisting of two substructures. The results showed that the correlation between the ultrasonic wave velocity and the molecular structure differs in different coalification stages. In the first stage (Rr = 0.6%–∼1.6%), the ultrasonic wave velocity of coal keeps decreasing during the maturation process due to the aromatization of the coal molecular structure and the cleavage of alkyl side chains. In the second stage (Rr = 1.6%–∼3.0%), the average layer size (La) of the coal molecular structure increases and the average interlayer space decreases, which makes the ultrasonic wave velocity of coal increase continuously. The evolution of the molecular structure of coal is an important influencing factor for its elastic properties. The irregular parts (alkyl side chains and functional groups) play a major role in elastic ultrasonic wave velocity, followed by the average layer size (La) and the average interlayer spacing (d) of aromatic layers. It was determined that the relationship between the coal rank and ultrasonic wave velocity of coal without macro-fractured can be interpreted as the evolution of the molecular structure (two substructures), and the ultrasonic velocity measurement methods were applied to investigate the coal structure. These relations can be useful for geophysical exploration of coal and coalbed methane.