A theoretical investigation is carried out to study the characteristic properties of dust-ion acoustic (DIA) shock waves in a magnetized, charge varying, complex (dusty) plasma which consists of immobile dust grains, fluid ions and superthermal electrons. The effects of collisions are not included here, but the dissipation leading to the formation of stable shock structures is provided by the dust charge fluctuations. The Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived using the reductive perturbation technique. The combined effects of obliqueness, magnitude of the magnetic field, and electron superthermality on the DIA shock waves are then investigated. It is shown that the effects of obliqueness, electron non-thermality and dust charge fluctuation significantly modify the basic properties of DIA shock waves.
