How Fast can a Grizzly Bear Run. Grizzly bears are able to run as fast as 55 km per hour. They seem to be more active at dawn and dusk, but may come out any time.Grizzly bears also share the same area of food provided the food is good enough to feed all of them.t is one of the most revered animals of North America. Grizzly is a sub-species of Brown bear. Black bears have claws that are almost two inches long whereas grizzlies have four inches long claws. These claws go white in time but there are also a few bears that have cream-colored claws. They are also expert swimmers.