Quantization will be necessary in the digital signal processing because of the hardware’s resource. It is important to improve the performance of the quantizer. An expression of quantization distortion to clip level was derived theoretical for N(μ,σ²)Gaussian pdf signal. Also the expression of the minimal quantization distortion and optimum clip level was deducted. The result of computer simulation is that the expression can be used to estimate the optimum clip level effectively and exactly in the related applications.