Recursive and non-recursive theoretical closed-form expressions of variable step-size incremental least mean square (VSSILMS) algorithm are derived in wireless sensor networks (WSNs). In fact, the theoretical transient and steady-state of the VSS 1 stand 2 nd-moment relations are derived in recursive and non-recursive closed forms adopting the initial design parameters only. Moreover, the tedious task of finding the simulation length can be implied by a quick simulation of the VSS 1s—moment closed-form having the initial design parameters alone in a prior to the real simulation. In the real simulations, the proposed theoretical 1st- and 2nd-moment closed forms are found in a good agreement with the empirical results.