True random number generators (TRNGs) have received extensive research owing to their wide applications in information processing, transmission, and encryption. Recently, TRNGs have also been employed in emerging stochastic/probabilistic computing paradigms. TRNGs can be designed based on, for example, oscillator sampling, noise amplifying, and quantum physical effect with the aid of peripheral postprocessing circuitry. With the rapid development of emerging nanoscale devices, such as resistive devices, spintronic devices, and photonic devices, a rich variety of TRNG prototypes have been proposed in the literature. Very recently, skyrmion has emerged as a promising candidate for implementing TRNGs because of the nanometer size and, more importantly, the intrinsic thermal Brownian motion dynamics. In this article, we propose for the first time a TRNG based on the continuous skyrmion thermal Brownian motion in a confined geometry at room temperature. Random bitstream (with equal probability of similar to 50% for bits "0" and "1") can be obtained by periodically detecting the relative position of the skyrmion without the need for any additional activations. Furthermore, we implemented a probability-adjustable TRNG, in which a desired probability for bit "0" and bit "1" can be acquired by adding an anisotropy gradient in the device through the voltage-controlled magnetic anisotropy (VCMA) effect. The behaviors of the proposed skyrmion-based TRNGs were studied by using micromagnetic simulations, and the generated random bitstream was tested by the National Institute of Standards and Technology (NIST) suits. Our results demonstrated that the proposed skyrmion-based TRNGs can achieve good randomness with high frequency (>1 GHz) and energy efficiency (< 10 fJ/bit).