This article presents thermoplastic sound-absorbing composites manufactured on the basis of renewable raw materials. Both the reinforcing material and the matrix material were biodegradable and used in the form of fibers. In order to mix flax fibers with polylactide fibers, the fleece was fabricated with a mechanical system and then needle-punched. The sound absorption of composites obtained from a multilayer structure of nonwovens pressed at different conditions was investigated. The sound absorption coefficient in the frequency ranging from 500 Hz to 6400 Hz was determined using a Kundt tube. The tests were performed for flat composites with various structures, profiled composites, and composite/pre-pressed nonwoven systems. Profiling the composite plate by convexity/concavity has a positive effect on its sound absorption. It is also important to arrange the plate with the appropriate structure for the incident sound wave. For the composite layer with an added pre-pressed nonwoven layer, a greater increase in sound absorption occurs for the system when a rigid composite layer is located on the side of the incident sound wave. The addition of successive nonwoven layers not only increases the absorption but also extends the maximum absorption range from the highest frequencies towards the lower frequencies.