Results of experimental studies on a H-2/air continuous rotating detonation engine (CRDE) in an annular combustor are presented. A tangentially injected H-2/O-2 hotshot jet is used to ignite the engine. H-2/air continuous rotating detonations are realized at a wide range of total mass flow and equivalence ratio conditions. The detonation propagation modes of all the tests can be divided into four kinds: two-wave, hybrid two/one wave, one-wave, and transient one wave. The mean propagation velocities of the two-wave and one-wave modes are in the range 1365-1476 m/s and 1606-1791 m/s, respectively. The propagation mode and velocity are influenced by both the total mass flow rate and equivalence ratio. Detonation wave propagation processes of the two-wave and one-wave modes are also observed, which further demonstrates the realization of CRDE.