In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive sequence of mappings and the set of solutions of the variational inequality for an inverse strongly monotone sequences of mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common fixed point of a nonexpansive sequence of mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a nonexpansive sequence of mappings and the set of zeros of an inverse-strongly monotone sequence of mappings.

metric projection, inverse-strongly monotone mapping, nonexpansive mapping, variational inequality, strong convergence.