A random bit stream generator which includes a pseudo-random bit stream generator and a multi-stage noise shaping (MASH) delta-sigma modulator is introduced. The pseudo-random bit stream generator may generate a first random bit stream according to a first clock signal. The MASH delta-sigma modulator is coupled to the first random bit stream generator to receive the first random bit stream and output a second random bit stream according to the first random bit stream and a second clock signal. A frequency of the second clock signal is greater than a frequency of the first clock signal, and the random bit stream has bell-shaped distribution. A method of generating a random bit stream having bell-shaped distribution adapted to a random bit stream generator is also introduced.