In this paper we introduce strongly (Vλ,A, Δnvm,p, q)-summable sequences and give the relation between the spaces of strongly (Vλ,A, Δnvm,p, q)-summable sequences and strongly (Vλ,A, Δnvm,p, q)-summable sequences with respect to a modulus function when A =(aik) is an infinite matrix of complex number, (Δnvm) is generalized difference operator, p = (pi) is a sequence of positive real numbers and q is a seminorm. Also we give the relationship between strongly (Vλ,A, Δnvm,p, q) - convergence with respect to a modulus function and strongly Sλ(A, Δn(vm))- statistical convergence.