The normalized subband adaptive filter (NSAF) algorithm has gained a large amount of attention owning to its fast convergence rate for correlated inputs. However, the convergence analysis of the NSAF algorithm has not been researched extensively, especially in the presence of noisy inputs which is frequently encountered in the applications of system identification and channel estimation. In this paper, we perform the performance analysis of the NSAF algorithm under noisy inputs. According to several reasonable assumptions and approximations, the expressions of the transient-state and steady-state mean-square deviation (MSD) are derived. Simulations under different kinds of environments confirm the accuracy of our theoretical expressions.