We consider the following neutral functional differential equation with piecewise constant delay:d²/dt²(x(t)+p(t)x(t-1))=qx(2［t+1/2])+g(t,x(t),x［t］)By using fixed point theorem and the method of pseudo-almost periodic sequence, we get the existence of the pseudo-almost periodic solution of this equation. Also, some results in reference ［5～8］ have been extended.