Laboratory experiments using a wave flume were designed to examine the threshold condition for ripple formation under asymmetrical oscillatory flows on an artificially roughened bed. Three types of sand beds were prepared in the experiments: they were flat, notched, and notch-mounded beds with bed roughness increasing in this order. The beds were constructed with three kinds of well-sorted sand with similar density, but different diameters. Data analyses were made using the two dimensionless parameters: the mobility number, M, a simplified form of the Shields number, and the Ursell number, U, a surrogate for asymmetry of flow field. The result confirmed that the threshold for ripple initiation is decreased with increasing bed perturbation and that as the bed perturbation increases, the dependency of this threshold on the flow asymmetry becomes less and finally null for the notch-mounded bed. This relationship is quantified by the following equations: M=17−14.5e−0.03U on the flat bed, M=5.0−2.5e−0.1U for the notched bed, and M=2.5 for the notch-mounded bed. A comparison between the previous field data and the present laboratory findings indicates that the threshold in the notch-mounded bed experiment, M=2.5, seems to provide a critical condition for rippling in the natural environment.