We study the influence of the incoherent pump field on the transient response of a three-level V-type system with two near-degenerate excited states. In this system due to interaction of the field with the vacuum an interference term appears, the spontaneously generated coherence term. We find that due to the incoherent pump the transient proprieties of the atomic system can be significantly modified. The enhancement of the transient gain can be obtained for proper values of the rate of the incoherent pump field and relative phase between the two fields.