Background: Handgrip strength (HGS) and the appendicular lean mass index (ALMI) are important determinants of sarcopenia. Muscle quality (MQ) is a measure of muscle strength relative to muscle mass. We examined trends in handgrip strength, the appendicular lean mass index, and analyzed their relationship with age, anthropometry, and body composition in a sample of participants in the United States (US). Methods: This cross-sectional study analyzed data from 14,741 US males (49.7%) and females (50.3%) 6–80 years old who responded to the National Health and Nutrition Examination Survey (NHANES) from 2011 to 2014. Dual X-ray absorptiometry was used to measure appendicular skeletal muscle mass. HGS was evaluated using the Takei Digital Grip Strength Dynamometer. Smoothed normative curves for HGS and the ALMI were constructed using a generalized additive model. Multiple regression analyses were used to examine associations of HGS and the ALMI with age, nutrition-related factors, physical activity, and body composition. Results: Mean HGS and the ALMI declined with advancing age. While mean HGS increased with the ALMI, it decreased with the fat mass index. HGS increased in males with an increase in body mass index, energy intake, the ALMI, and vitamins; however, HGS in females increased with albumin, but it had a negative association with the fat mass index and age, but not with increasing adiposity. Conclusions: HGS and the ALMI change with age: HGS increases with age, then stabilizes and declines; the ALMI increases with age, then stabilizes. In addition, we provide evidence for the effect of anthropometry, nutrition, physical activity, and body composition on HGS and the ALMI in US population.