An electrical device mounting structure on a motorcycle which includes a resilient support member having a spring-flexural resilience and supporting an electrical device unit. The resilient support member has a first portion secured to a vehicle body or a member connected to the vehicle body. The resilient support member also has a second portion provided separate from the first portion and closer to the electrical device. The second portion is supported on the vehicle body or the member connected to the vehicle body via an elastic member having an attenuating property.