Some sufficient conditions are established for the oscillation of second-order neutral differential equation (x(t)+p(t)x(τ(t)))′′+q(t)f(x(σ(t)))=0, t≥t0, where 0≤p(t)≤p0<+∞. The results complement and improve those of Grammatikopoulos et al. Ladas, A. Meimaridou, Oscillation of second-order neutral delay differential equations, Rat. Mat. 1 (1985), Grace and Lalli (1987), Ruan (1993), H. J. Li (1996), H. J. Li (1997), Xu and Xia (2008).