In ion-ripple wiggler, with changing the direction of the injected electron beam, the longitudinal component of the ion-ripple electric field equals to zero, thereby, the harmful influence of longitudinal electric field of an ion-ripple wiggler can be eliminated. Under the condition of small amplitude, the operating equations of the wiggler are given, and then, the trajectories of the beam electrons, the angular spectrum of spontaneous emission and small signal gain are derived.