In this study, we examine the condition of the conchoidal surface to be a Bonnet surface in Euclidean 3-space. Especially, we consider the Bonnet conchoidal surfaces which admit an infinite number of isometrics. In addition, we study the necessary conditions which have to be fulfilled by the surface of revolution with the rotating curve c(t) and its conchoid curve c(d)(t) to be the Bonnet surface in Euclidean 3-space.