Several sensing techniques have been proposed for silent speech recognition (SSR); however, many of these methods require invasive processes or sensor attachment to the skin using adhesive tape or glue, rendering them unsuitable for frequent use in daily life. By contrast, impulse radio ultra-wideband (IR-UWB) radar can operate without physical contact with users' articulators and related body parts, offering several advantages for SSR. These advantages include high range resolution, high penetrability, low power consumption, robustness to external light or sound interference, and the ability to be embedded in space-constrained handheld devices. This study demonstrated IR-UWB radar-based contactless SSR using four types of speech stimuli (vowels, consonants, words, and phrases). To achieve this, a novel speech feature extraction algorithm specifically designed for IR-UWB radar-based SSR is proposed. Each speech stimulus is recognized by applying a classification algorithm to the extracted speech features. Two different algorithms, multidimensional dynamic time warping (MD-DTW) and deep neural network-hidden Markov model (DNN-HMM), were compared for the classification task. Additionally, a favorable radar antenna position, either in front of the user's lips or below the user's chin, was determined to achieve higher recognition accuracy. Experimental results demonstrated the efficacy of the proposed speech feature extraction algorithm combined with DNN-HMM for classifying vowels, consonants, words, and phrases. Notably, this study represents the first demonstration of phoneme-level SSR using contactless radar.