Of late, the frequent use of composite materials merits effective inspection techniques to ensure structural integrity after manufacturing as well as during service. The inspection of composite materials is undertaken using various nondestructive testing (NDT) techniques. Ultrasonic testing (UT) is one of the popular NDT techniques used for testing of composites. The aim of the research is to establish a quantitative relationship between UT signal’s features and the mechanical property, i.e., impact toughness of the composite material heat treated at different temperatures. Polyester glass fiber–reinforced composite undergone post-cure heat treatment is the composite used in the research work. The glass fiber–reinforced plastic (GFRP) specimens have been heat treated at different temperatures to mimic different levels of thermal aging. The impact toughness of the composite material is determined using the Charpy impact test. Then, variation in attenuation of UT signals is related to the change in impact toughness of GFRP composite material heat treated at different temperatures. A possible classification of UT signals acquired from GFRP specimens in terms of different level of thermal aging has also been investigated through application of Hilbert–Huang transform (HHT) on the acquired UT signals. Hilbert energy frequency distribution-based feature extraction has been successfully used to analyze the effect of post-cure heat treatment on GFRP composite. An empirical relationship is finally obtained between Charpy impact energy and HHT energy. The proposed technique will be useful in prediction of strength and remaining useful life of GFRP composites through analyses of acquired UT-based NDT signals.