The zero attracting normalized least mean square (ZA-NLMS) algorithm achieves lower steady-state error than the normalized least mean square (NLMS) algorithm for sparse system identification. Most of the available analytical results on several versions of the zero attracting least mean square algorithms assume white Gaussian inputs. This paper presents the individual weight error variance (IWV) analysis of the ZA-NLMS algorithm without Gaussian inputs assumption. The IWV analysis is based on exact individual weight error relation and used to derive the transient and steady-state behavior of the ZA-NLMS algorithm without restricting the input to being Gaussian or white, whereas some assumptions are introduced to overcome weight nonlinearity in evaluating certain expectations involved. Extensive simulations are used to verify the analysis results presented.