By means of Liapunov's direct method coupled with Razumikhin technique some sufficient conditions for (uniform, uniform and globally asymptotic, uniformly globally asymptotic, and globally exponential) p-moment stability of the zero solution of functional differential equations with random impulses are presented, where the parameter λ( t) in (d V( t, x( t)))/d t is not required to be negative definite. Thus the obtained results are convenient to apply.