The properties of volume holograms recorded with speckle reference wave are of interest because they allow high-density information multiplexing and its coding and processing. The results of theoretical and experimental study of angular selectivity for this type of hologram are presented in this article. Several mechanisms are interacting in this case as a result of the joint action of cross modulation grating (diffraction on cross grating) and intermodulation structure (locally recorded speckle pattern). The conditions are determined when the value of the angular selectivity depends either on the cross grating spacing or on the speckle pattern parameters. The strong angular selectivity of the speckle-wave hologram can be observed by its angular detuning in any arbitrary direction. It is demonstrated that observed peculiarities in the character of angular selectivity of the hologram with reference speckle wave can be very efficient for multiple holographic image recording in thick media.