The Musandam group is comprised of a sequence of carbonate sediments deposited in the area of the present Northern Emirates between the Jurassic and lower Cretaceous. This rock is important both regarding hydrocarbon reservoirs and civil infrastructure. Consequently researchers have performed much systematic experimental work. However, the creep behavior of Musandam limestone fractures under confining pressures has not been very well characterized so far. This paper presents the results of an initial experimental study of the creep behavior of fractures in Musandam limestone at confining pressures less than 1 MPa. The experimental study systematically investigates the fracture creep under different confining pressures and flowrates by conducting fracture flow tests in a triaxial system. In addition, the mechanisms underlying the permeability evolution were also examined to some extent. The results indicate that the fracture hydraulic conductivity decreases with time. Increasing the confining pressure or flowrate or surface roughness leads to greater hydraulic aperture reduction. Also, the effect of mechanical compression on specimen (the fracture and rock matrix) creep is not negligible.