This letter develops theoretical analysis of the normalized LMS algorithm (NLMSA) for use in complex-domain adaptive filters in the presence of impulse noise at filter input. We propose a new "stochastic" model for such impulse noise, and assume that filter reference input process is a white process, e.g., digital QAM data, White & Gaussian process, etc. In the analysis, we derive a simple difference equation for mean square tap weight misalignment (MSTWM). Experiment is carried out to demonstrate effectiveness of the NLMSA in robust filtering in the presence of the impulse noise at the filter input. Good agreement between simulated and theoretically calculated filter convergence, in a transient phase as well as in a steady-state, proves the validity of the analysis.