Since de Moivre and Gauss proved central limit theorems,normal distributions (also Gaussian distributions) has been occupied a "central" position in probability theory. The classical central limit theorem indicates that a group of random variables will uniformly converge to normal distributions under IID framework. As an application,the central limit theorem is widely used in financial risk prevention and calculation (for example Basel IV). A natural question is whether normal distribution still occupies a "central" position in quantum theory or non-IID framework. To answer this question, this paper investigates the central limit theorem for three-state quantum walks on the real line. We introduce a set of special unitary operators-the rotation matrix, whose degrees of freedom include rotation axis and angle.