The Degasperis-Procesi(DP) equation describing the propagation of shallow water waves contains a physical parameter ω,and it is well-known that the DP equation admits solitary waves with a peaked crest when ω = 0.In this article,we illustrate,for the first time,that the DP equation admits peaked solitary waves even when ω 0.This is helpful to enrich our knowledge and deepen our understandings about peaked solitary waves of the DP equation.