IMO it's too young in our experience.
The first part of the museum is about spy stuff - gadgets, cars, that kind of thing. My guess is 10 and up would enjoy that part the most, younger would get something out of it but could be bored pretty quickly. The rest of the museum (a good half of it) is about spying in the 20th century and beyond. There's a lot of world history involved in this part - WWII, dropping of the atomic bomb, Cold War, that kind of thing. Not the type of thing that your typical young kid would enjoy especially considering the admission fee charged!