In this paper, we consider the coding of an independent and identically distributed (i.i.d.) Gaussian source with side information available only at the decoder in the form of a noisy version of the source to be encoded. This problem is known as Wyner-Ziv coding in literature. In this paper, we propose concrete implementation by using the strategy of multi-dimensional nested lattice quantization (NLQ). By investigating various lattices in the dimensions considered, we give some analysis on how lattice properties affect performance. We also propose a method on choosing good coarse lattices in multiple dimensions. By introducing scale factors, we examine the relationship between distortion and scale factor for various rates. As dimension increases to eight and twenty-four, we obtain distortion performance close to the Wyner-Ziv limit. Meanwhile, our scheme is simple without causing long delay and large storage, which is suitable for sensor networks.