In this paper we propose a novel piecewise uniform scalar quantizer model designed for a Gaussian memoryless source. The segment thresholds of this quantizer model are equidistant while the number of reproduction levels inside segments is determined by optimizing the inner distortion and under the constraint of total number of reproduction levels. For the proposed quantizer model the quantization efficiency and signal to quantization noise ratio (SQNR) is studied. On the basis of the comparison with the efficiency and SQNR of uniform quantizer advantages of the proposed quantizer model are shown. Particularly, it is shown that with the proposed quantizer the correlation between the input signal and the quantization error can be eliminated more than by using the uniform quantizer as well as that the proposed quantizer provides higher level of SQNR.