This paper presents a mathematical model for the oscillator-based true random number generator (TRNG) to study the influence of some key parameters to the randomness of the output sequence. The output of the model is so close to the output of the real design of the TRNG that the model can generate the random bits instead of the analog simulation for research. It will cost less time than the analog simulation and be more convenient for the researchers to change some key parameters in the design. The authors give a method to improve the existing design of the oscillator-based TRNG to deal with the possible bias of the key parameters. The design is fabricated with a 55-nm CMOS process.