We study the nonlinear Schrödinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψt+Δψ +φ(ωt)|ψ|αψ+iζ(ωt)ψ= 0.Under some conditions, we show that as ω→∞, the solution ψω will locally converge to the solution of the averaged equation iψt+Δψ +φ0|ψ|αψ+iζ0ψ= 0 with the same initial condition in Lq((0, T),Brs,2)for all admissible pairs (q, r), where T ∈ (0,Tmax). We also show that if the dissipation coefficient ζ0 large enough, then,ψω is global if ω is sufficiently large and ψω converges to ψ in Lq((0,∞),Brs,2), for all admissible pairs (q, r). In particular, our results hold for both subcritical and critical nonlinearities.